A229239 Total number of parts in all partitions of n^2 into squares.

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

Adjacent sequences: A229236 A229237 A229238 * A229240 A229241 A229242

Keyword

nonn

Author

Christopher Hunt Gribble, Sep 23 2013

Status

approved