A332716 Number of compositions of n^2 where each part is less than or equal to n.

1, 1, 5, 149, 20569, 11749641, 26649774581, 236837126431501, 8237168505776637425, 1125036467745713090813969, 606147434557459526483161067501, 1293596348252277644272081532560154645, 10970544241076481629439275072320816659677161

Offset: 0

Author

Alois P. Heinz, Feb 20 2020

Keywords

• nonn

Comments

All terms are odd.

Examples

			a(2) = 5: 22, 211, 121, 112, 1111.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..57

Crossrefs

Cf. A000079, A000290, A008464, A048004, A090667, A103488, A332721, A332796.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1,
      add(b(n-d, k), d=1..min(n, k)))
    end:
a:= n-> b(n^2, n):
seq(a(n), n=0..15);

Mathematica

b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - d, k], {d, 1, Min[n, k]}]];
a[n_] := b[n^2, n];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Oct 31 2022, after Alois P. Heinz *)

Formula

a(n) = Sum_{i=0..n-1} A048004(n^2-1,i) for i > 0.