A298640 Number of compositions (ordered partitions) of n^2 into squares > 1.

1, 0, 1, 1, 2, 8, 12, 129, 874, 9630, 167001, 3043147, 72844510, 2423789655, 106665874384, 6156805673648, 470151743582651, 47558937432498729, 6363358599941131580, 1126147544855148769425, 263646401550138303553708, 81649922556593759124887197

Offset: 0

Author

Ilya Gutkovskiy, Jan 24 2018

Keywords

• nonn

Examples

			a(5) = 8 because we have [25], [16, 9], [9, 16], [9, 4, 4, 4, 4], [4, 9, 4, 4, 4], [4, 4, 9, 4, 4], [4, 4, 4, 9, 4] and [4, 4, 4, 4, 9].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..128
• Index entries for sequences related to sums of squares
• Index entries for sequences related to compositions

Crossrefs

Cf. A000290, A006456, A078134, A224366, A280542, A298642.

Programs

Maple

b:= proc(n) option remember; `if`(n=0, 1,
      add(b(n-j^2), j=2..isqrt(n)))
    end:
a:= n-> b(n^2):
seq(a(n), n=0..25);  # Alois P. Heinz, Feb 05 2018

Mathematica

b[n_] := b[n] = If[n == 0, 1, Sum[b[n - j^2], {j, 2, Floor @ Sqrt[n]}]];
a[n_] := b[n^2];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, May 21 2018, after Alois P. Heinz *)

Formula

a(n) = [x^(n^2)] 1/(1 - Sum_{k>=2} x^(k^2)).

a(n) = A280542(A000290(n)).