paper (pdf), related among others to OEIS A034807. arXiv:2304.12937 [math.CO].
paper (pdf), related among others
to OEIS A075513.
paper (pdf), related among others
to OEIS A333852.
paper (pdf), related to OEIS A334430, arXiv:2008.04300 [math.NT] .
paper (pdf), related among others
to OEIS A324251.
paper (pdf) related to:
OEIS A324038
paper (pdf), related among others
to OEIS A296181.
paper (pdf), related among others to OEIS A300068.
paper (pdf), related among others
to OEIS A305310.
paper (pdf), arXiv:1810.09787 [math.NT] .
paper (pdf), related among others to OEIS A321331
Table with notes (pdf), related to OEIS A282624.
paper, (pdf) with updates, related, among others, to OEIS A282629. See also the
ArXiv version.
paper, (pdf) with updates, related, among others, to OEIS A288875. See also the
ArXiv version.
paper, (pdf), related, among others, to
OEIS A290596.
Paper (pdf) related
among others to: OEIS A268922.
Paper (pdf) related
among others to:
OEIS
A273506, OEIS
A275790, OEIS A275791.
Paper (pdf) related to:
OEIS A057059.
Paper (pdf) related to:
OEIS A249869
Paper (pdf) related
among others to:
OEIS A251629.
Paper (pdf) related among others to:
OEIS A001132.
Paper (pdf) related among others to:
OEIS A255240.
Paper (pdf) related among others to:
OEIS A256099.
Paper (pdf) related among others to: OEIS A007969.
Paper (pdf) related among others to:
OEIS A007970.
Paper (pdf) related among others to: OEIS A239126.
See also the ArXiv version.
Paper (pdf) related among others to: OEIS A002580.
See also the ArXiv version.
Paper (pdf) related among others to:
OEIS A249870.
Notes (pdf) for OEIS
A220674.
the Pell +/-4 Equations", July 2013. January 2023 Paper (pdf) for OEIS A225953.
Notes (pdf) for OEIS
A212359 . See also OEIS A212359 .
Notes (pdf) for
OEIS A213939.
See also OEIS A213941.
Notes (pdf)
for OEIS A213938 .
Notes (pdf)
for OEIS A215037 .
Paper (pdf) related mainly to:
OEIS A187360. See also the
ArXiv version.
Published in
The Fibonacci Quarterly, Vol.42,3 (August 2004) pp 231-244
revised version, July 1999 paper
(.ps.gz file, 10 pages)
revised version, May 2000 paper
(.ps.gz file, 12 pages, including a table)
Published in
The Fibonacci Quarterly, Vol.38,5 (2000) pp 408-419
revised version, May 2000 paper
(.ps.gz file, 14 pages, including three tables)
sec. revised version, June 2001 paper
(.ps.gz file, 15 pages, including three tables)
Published in
The Fibonacci Quarterly, Vol.40,4 (2002) pp 299-313
2019
"A list of representative simple difference sets of the Singer type for small orders m", July 2020
"On the Equivalence of Three Complete Cyclic Systems of Integers",
August 2020
2019
"Cycles of reduced Pell forms, general Pell equations and Pell graphs", April 2019
"Collatz Trees from Vaillant-Delarue Maps", May 2019
"Memoir on Napoléon's Theorem", October 2019
2018
"Notes on the Discrete Theodorus Spiral", January 2018
"On a Conformal Mapping of Regular Hexagons and the Spiral of its Centers", March 2018
"A Note on Markoff Forms Determining Quadratic Irrationals with Purely Periodic Continued Fractions", July 2018
"The Tribonacci and ABC Representations of Numbers are Equivalent", October 2018, revised September 2020
"On the Generating Functions of the Boas-Buck Sequences for the Inverse of Riordan and Sheffer Matrices", December 2018
2017
"Table for the multiplicative group of integers modulo A033949 ", March 2017
"On Sums of Powers of Arithmetic Progressions, and Generalized Stirling, Eulerian and Bernoulli Numbers ", July 2017
" On Generating Functions of Diagonal Sequences of Sheffer and Riordan
Number Triangles ", August 2017
" Note on a- and z-sequences of Sheffer number triangles for certain generalized Lah numbers ", Seprtember 2017
2016
"Note on a Recurrence for Approximation Sequences of p-adic Square Roots", March 2016
"Expansions for phase space coordinates for the plane pendulum", August 2016
"Proof of a Conjecture Involving Chebyshev Polynomials", September 2016
"A Note on the Area Table A249869 for Primitive Pythagorean Triangles ", November
2016
2015
"On lattice point circles for the Archimedean tiling (4,8,8)",
January 2015
"Primes +1 (mod 8) or -1 (mod 8) and Sum of Legs of Primitive Pythagorean Triangles",
February 2015
"Archimedes's Construction of the Regular Heptagon", March 2015
"A Geometrical Problem of Omar Khayyám and its Cubic", April
2015
With Kival Ngaokrajang: "Certain 'connected' binary bisymmetric n X n
matrices", Examples for n = 1, ..., 6, August 2015
"Proof of a Conjecture Related to the 1-Happy Numbers", September
2015
"Proof of a Theorem Related to the Happy Number Factorization",
October
2015
2014
"Collatz' Words, Sequences and Trees", April 2014
Published in Journal of
Integer Sequences Vol. 17 (2014) 14.11.7
"Notes on Some Geometric and Algebraic Problems Solved by Origami", September 2014
"On lattice point circles for the Archimedean tiling (3,4,6,4)", December 2014
2013
`"Albrecht Dürer's approximation of a regular
5-gon", Januar 2013
`"Periods
of Indefinite Binary Quadratic Forms, Continued Fractions and
2012
"Partition Array for the Number of Representative Necklaces", June
2012
"Partition Array for the Number of Representative
Bracelets", July 2012
" Two Lists of Multiset Representatives", July 2012
" Application of the Partial Summation Formula to some Sums over Cubes of Fibonacci Numbers", August 2012
"The field Q(cos(pi/n)), its Galois group, and length ratios in
the regular n-gon ", October 2012, Revised version: March 2011.
2011
" A181875/A181876. Minimal Polynomials of cos(2π/n)", January 2011
" A181872/A181873. Minimal Polynomials of sin(2π/n) ", January 2011
"Divisor Product Representation for Natural Numbers ",
February 2011
"Ordinary Generating Functions for Sums of Powers of the First n
Positive Integers ", October 2011
"Counting Walks on Jacobi Graphs: An Application of Orthogonal Polynomials ", November 2011
2010
"Simple proofs of some facts related to the Bell sequence and
triangle A007318 (Pascal) and A071919 (enlarged Pascal) ", June 2010
" A176740: E.g.f. Lagrange Inversion Partition Array ", July 2010
" Notes on certain inhomogeneous three term recurrences ", September 2010
" A181347/A181348. Logarithm of the Fibonacci matrix A037027 ",
October 2010
" A181878, Coefficient array for square of Chebyshev S-polynomials ",
December 2010
2008
" Combinatorial Interpretation of Generalized Stirling Numbers ", October 2008
preprint KA-TP-28-2008 (pdf)
(.ps.gz)
corrected and restyled version, March 2009.
Published in Journal of Integer Sequences Vol. 12 (2009) 09.3.3
2005
" Two Normal Ordering Problems and Certain Sheffer Polynomials ", July 2005
DESFA talk (extended), Munich, July 28, 2005
preprint KA-TP-13-2005 (pdf)
preprint KA-TP-13-2005 (.ps.gz)
Some misprints corrected, May 21, 2007.
Published in the Proceedings Difference Equations, Special Functions and
Orthogonal Polynomials, edts. S. Elaydi et al., World Scientific, 2007, pp.
354-368.
For the correction of a misprint on p.359, formula after 'A recurrence is
given by', see the above corrected preprint version.
2004
" Chebyshev Polynomials and Certain Quadratic Diophantine Equations ",
KA-TP-07-2004, September
abstract (TeX file),
abstract (.ps.gz file),
abstract (.pdf file),
title (TeX file),
title page (LaTeX file),
title page (.ps.gz file),
title page (.pdf file),
paper (.ps.gz file,9 pages and 4 tables),
paper (.pdf file, including four tables).
Four Tables (.ps.gz file, 4 pages).
Four Tables (.pdf file).
2001
" Riccati meets Fibonacci",
KA-TP-11-2001, June
abstract (TeX file),
abstract (.ps file),
title (TeX file),
title page (LaTeX file),
title page (.ps file),
title page (.html file),
paper (.ps.gz file, 14 pages),
paper (.html file).
revised paper, Sept. 2002 (.ps.gz file).
2000
"On Generalizations of the Stirling Number Triangles ",
KA-TP-1-2000, February, latest version June 2000
abstract (TeX file),
abstract (.ps file),
title page (.ps file),
title page (.html file),
title page (LaTeX file),
paper (.ps.gz file, 20 pages, including
four tables, corrections Oct 15 2007),
four k-Stirling tables
(.html file with links to N. J. A. Sloane's EIS)
Published in
Journal of Integer Sequences Vol.3 (2000) 00.2.4
Note added, Jan 23, 2008: The generalized Stirling numbers of the second
kind S2(k->a+1;n,m->l) appear as P_{n,l}(a) in Example 4, p. 167 of the 1973 paper " Une formule explicite pour les puissances successives de
l'opérateur de dérivation de Lie " by Louis Comtet.
Comptes Rendus Acad. Sc. Paris, 276 A (1973) 165-168.
Eqs. (10), (11) and (12) of this ref. give the e.g.f., an explicit formula and
the recurrence.
Note added, Jan 31, 2008: The numbers S2(k;n,m) appear already as special
case in the article
Leonard Carlitz: On arrays of Numbers. Am. J. Maths. Vol.54 No. 4 (Oct.,1932), pp 739-752
Put μ = 1 and λ = k-1 in the recurrence, eq. (4), for a_{n,s} with s->m.
Note added, Sep 29, 2011: The numbers S2(k;n,m) appear already in the
Göttingen 1823 dissertation of H. F. Scherk in sect. 9,
III,pp.30-31, as a^m_n (with suppressed k=p dependence)
H. F. Scherk:
De evolvenda functione ... disquisitiones nonnullae analyticae , sect. 9,
III,pp.29-31.
This reference has been found by M. Mohammad-Noori: Some remarks about
the derivation operator and generlized Stirling numbers, 2010 ,
see ref. [9].
This dissertation is discussed in Appendix A of the paper
P. Blasiak and Ph. Flajolet:
Combinatorial Models of Creation-Annihilation, 2011 , see ref. [112], and
p.76, Proposition A.3. Thanks go to Thomas Copeland for pointing out this paper
by e-mail Jun 04 2011.
Note added, Mar 18, 2014: The formula exp(g(x)d/dx)u(x) =
u(G^{(-1)}[G(x)+1]) with G(x) = int(1/g(x),x) is credited to C. Graves: A
Generalization of the Symbolic Statement of Taylor's Theorem, Proc. of
Royal Irish Academy, vol. 5 (1850-1853), pp. 285-287,
in the book by Harold T. Davis, The Theory Of Linear Operators, 1936,
The Principia Press, p. 13 and p. 588. Thanks go to Thomas Copeland for
pointing out the Davis book by e-mail Mar 09 2014.
1998
"On Polynomials Related to Powers and Derivatives of the
Generating Function of Catalan's Numbers" ,
KA-TP-4-1998, April
abstract (LaTeX file)
abstract (.ps file)
title page (.ps file)
paper (.ps.gz file, 20 pages, including
three tables)
"On Polynomials Related to Powers of the
Generating Function of Catalan's Numbers" ,
"On Polynomials Related to Derivatives of the
Generating Function of Catalan Numbers" ,
1997
"On Sums of Powers of Zeros of Polynomials" ,
KA-TP-2-1997, May
abstract (.tex file)
abstract (.ps file)
title page (.ps file)
paper (.ps.gz file, 22 pages, including
two tables)
Published in "Journal of Computational and Applied Mathematics",
88 (1998) 237-256
Sevilla-talk(.ps.gz file, 12 pages)
See Some
links and Scans under the year 2006 for `Albert Girard and the
Waring Formula' for historical remarks.
1996
" The Measure of the Orthogonal Polynomials Related to Fibonacci
Chains: The Periodic Case" , KA-TP-1-1996, January
Revised version of an earlier paper with the same title.
abstract (.ps file)
paper (.ps.gz file, 19 pages)
figure 1 (.ps.gz)
figure 2 (.ps.gz)
figure 3 (.ps.gz)
published in: Journal of Physics A, 29 (1996) 4169-4185
Corrigendum (.ps.gz)
Published in JPhA 30 (1997) 765
"A Fibonacci Fractal: a Bicolored Self-Similar Multifractal
" , KA-TP-15-1996, May
abstract (.ps file)
paper (.ps.gz file, 16 pages)
figure 1 (.ps.gz)
figure 2 (.ps.gz)
figure 3 (.ps.gz)
figure 4 (.ps.gz)
figure 5 (.ps.gz)
figure 6 (.ps.gz)
Figures 5 and 6 scanned, originals on request
Published in "Applications of Fibonacci Numbers", Vol.7, pp 221-237
Edts.: G.E. Bergum, A.N. Philippou, and A.F. Horadam,
Kluwer, Dordrecht, 1998
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