W. Lang: Formatting of sequences

2001, updated for maple12: Feb 2009, new OEIS adaption Nov 2010, Mar 2012

March 2016: Unfortunately this program is no longer running on this machine. Sorry fo\ r this!

Formatting OEIS   tabl and tabf arrays

lower triangular matrix (tabl),   staircase matrix (tabf)

offset for rows and columns (integers):           

Id-number for output caption (will be the OEIS A-number if used in 'a-sequence' below)   

type in the OEIS A-number for 'a-sequence' type in the tabl or tabf sequence for 'a-sequence'

a-sequence: 

If the 'tabl' option is valid skip the next parts, go to 'Chose width of the output page', then 'SEND'.

For tabf arrays a second sequence, called the tabf shape sequence, is needed:

either row length sequence,   or step length sequence

type in the OEIS A-number for the 'shape sequence' of the chosen type type in the the 'shape sequence' of the chosen type use row length sequence [1,3,5,7,9,11,13,15,17,19,21] use row length sequence [1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8] use step length sequence [1,2,2,2,2,2,2,2,2,2] use step length sequence [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]

shape sequence: 
Entry irrelevant if preset shape sequence from pull down menue has been chosen.

Chose width of output page (e.g. 90)    

     

RESTORE EXAMPLE

Explanations:

• Select either 'tabl', if the 'a-sequence' should be formatted as a lower triangular matrix arrays , or 'tab\ f' for other (irregular) arrays.
• The output will have numbered rows and columns starting with the two 'off set' values. The default values are [0,0].
• The output caption will quote the 'Id-number' (with an 'A' in front). It will automatically be the OEIS A-number if this option is chosen for the 'a-sequence'.
• The 'a-sequence' input can be an OEIS A-number representing the tabl or tabf sequence as defined in OEIS under 'Keywords'.
  If a sequence is typed in (use the pull down menue for 'a-sequence'), it should be a string of integers, enclosed by brackets [ ] and separated by commas (insensitive to blanks, no comma at the end), representing a tabl or tabf sequence.
  
• For 'tabf' arrays a 'shape sequence' is needed in addition to the 'a-sequence'. One can choose either the row lengths or the step widths (the difference of the number of entries in consecutive rows, starting with the number of entries of the first row). No negative numbers are allowed for row lengths sequence entries.
  
• The width of the output page entry (in number of characters) influences the row number of the output array (tabl or tabf type).

The output will be a complete matrix type array (the 'alist' string is cut off, depeding on the 'shape sequence' which in the tabl case is the sequence of ten 1's). If the OEIS A-number for 'a-sequence' or the tabf shape sequence is known one could use also the 'type in ...' option and paste and copy from the OEIS files. One can get the sequence, say A000108, from the address http://oeis.org/A000108.

Acknowledgements:

This application would not exist without advice and help from Bernd Feucht, Gerrit Jahn, Christian Kaufhold, Andreas Maier, Richard Mathar, Christoph Mayer, and especially, from Drs. Thomas Hahn and Peter Marquard. Thanks go also to Dr. N. J. A. Sloane who suggested to allow as input also OEIS A-numbers as well as row length sequences in the tabf case.

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