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

Author

Christopher Hunt Gribble, Sep 23 2013

Keywords

• nonn

Examples

			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.
		

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

Crossrefs

Row sums of A229468.

Cf. A037444.

Programs

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 *)