# [seqfan] Re: a question about triangular numbers

Richard Mathar mathar at strw.leidenuniv.nl
Sat Dec 12 23:26:42 CET 2009

```Hijacking http://list.seqfan.eu/pipermail/seqfan/2009-December/003182.html :

There is a similar sequence defined as "The maximum square part while partitioning
n=x^2+y^2+z^2 into any three perfect squares (-1 of there is no such triple of squares)"
which starts at n=1 as

1, 1, 1, 4, 4, 4, -1, 4, 9, 9, 9, 4, 9, 9, -1, 16, 16, 16, 9, 16, 16, 9, -1,
16, 25, 25, 25, -1, 25, 25, -1, 16, 25, 25, 25, 36, 36, 36, -1, 36, 36, 25,
25, 36, 36, 36, -1, 16, 49, 49, 49, 36, 49, 49, -1, 36, 49, 49, 49, -1, 36,
49, -1, 64, 64, 64, 49, 64, 64, 36, -1, 64, 64, 64, 49, 36, 64, 49, -1, 64

Example for n=10 is 10=0+1+9, max(0,1,9)=9
Example for n=11 is 11=1+1+9, max(1,9)=9
Example for n=12 is 12=4+4+4, max(4)=4
Example for n=13 is 13=0+4+9, max(0,4,9)=9
Example for n=18 is 18=0+9+9 = 1+1+16, max(0,9,1,16)=16

See A004215 for locations of the -1, equivalent to location of zeros in A000164..
The sequence is not "nice" because the -1 destroy all of the squared beauty. -:)
This sequence may already appear somewhere in the OEIS in the department
of "tilings, floor-tiler aids, partitions, fractions, and other broken or
deliberately dissected and exploded parts, ..." BTW, ought there be a Wiki
(anti)-section with
(i) the most blatant abuse of (otherwise innocent unless proven to the
contrary) numbers?
See <a href="http://www.math.utah.edu/~cherk/mathjokes.html">Math jokes</a>
and <a href="http://www.math.ualberta.ca/~runde/jokes.html">Math Jokes</a>
(ii) the  most quickly dis-proved conjectures?
(iii) a section to papers that most often contra-cite the OEIS in the style
of "but this sequence is not (yet) mentioned /found in Sloane's ..." ?

RJM

```