login
A229239
Total number of parts in all partitions of n^2 into squares.
3
0, 1, 5, 19, 64, 206, 616, 1766, 4836, 12910, 33248, 83768, 205693, 495357, 1169030, 2713262, 6193247, 13932454, 30905452, 67684181, 146439145, 313266730, 663004212, 1389106622, 2882712626, 5928222338, 12086570971, 24440494114, 49035791349, 97646904849
OFFSET
0,3
LINKS
Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..689 (terms 0..200 from Alois P. Heinz)
Christopher Hunt Gribble, C++ program
EXAMPLE
a(2) = 5 because there are 5 parts in the set of partitions of 2^2 into squares. The partitions are (1 2 X 2 square) and (4 1 X 1 squares) giving 5 parts in all.
MAPLE
b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, [0$2],
b(n, i-1)+`if`(i^2>n, [0$2], (g->g+[0, g[1]])(b(n-i^2, i)))))
end:
a:= n-> b(n^2, n)[2]:
seq(a(n), n=0..40); # Alois P. Heinz, Sep 23 2013
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[i<1, {0, 0}, b[n, i-1] + If[ i^2 > n, {0, 0}, Function[g, g + {0, g[[1]]}][b[n - i^2, i]]]]]; a[n_] := b[n^2, n][[2]]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Nov 11 2015, after Alois P. Heinz *)
CROSSREFS
Row sums of A229468.
Cf. A037444.
Sequence in context: A211842 A304134 A318946 * A296330 A304162 A001870
KEYWORD
nonn
AUTHOR
STATUS
approved