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

0,3

Comments

All terms are odd.

Links

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

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A352758 A226803 A362494 * A230666 A113560 A094364

Adjacent sequences: A332713 A332714 A332715 * A332717 A332718 A332719

Keyword

nonn

Author

Alois P. Heinz, Feb 20 2020

Status

approved