A093116 Number of partitions of n^2 into squares not less than n.

1, 1, 1, 1, 2, 2, 2, 1, 2, 5, 4, 4, 5, 9, 15, 23, 24, 13, 20, 32, 55, 84, 113, 185, 303, 545, 167, 298, 435, 716, 1055, 1701, 2584, 4213, 6471, 10218, 15884, 4856, 7376, 11231, 17221, 26054, 39583, 60109, 91622, 138569, 209951, 318368, 483098, 730183

Offset: 0

Author

Reinhard Zumkeller, Mar 21 2004

Keywords

• nonn

Examples

			n=10: 10^2 = 100 = 64+36 = 36+16+16+16+16 = 25+25+25+25, all other partitions of 100 into squares contain parts < 10, therefore a(10) = 4.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A093115, A092362, A001156, A037444, A078134.

Cf. A072213, A161408. [Reinhard Zumkeller, Jun 10 2009]

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1,
     `if`(i^2>n, 0, b(n, i+1) +b(n-i^2, i)))
    end:
a:= proc(n) local r; r:= isqrt(n);
      b(n^2, r+`if`(r^2Alois P. Heinz, Apr 15 2013

Mathematica

b[n_, i_] := b[n, i] = If[n==0, 1, If[i^2>n, 0, b[n, i+1] + b[n-i^2, i]]]; a[n_] := With[{r = Sqrt[n]//Floor}, b[n^2, r + If[r^2Jean-François Alcover, Oct 26 2015, after Alois P. Heinz *)