A332796 Number of compositions of n^2 into parts >= n.

1, 1, 2, 6, 26, 140, 882, 6349, 51284, 457704, 4459940, 47019819, 532485538, 6438774524, 82710138994, 1123798871990, 16090426592488, 241979954659728, 3811335657375786, 62712512310820402, 1075527196672980525, 19186234784992217621, 355349469934379290700

Offset: 0

Author

Alois P. Heinz, Feb 24 2020

Keywords

• nonn

Examples

			a(0) = 1: (), the empty composition.
a(1) = 1: 1.
a(2) = 2: 22, 4.
a(3) = 6: 333, 36, 63, 45, 54, 9.
a(4) = 26: 4444, 556, 565, 655, 466, 646, 664, 457, 475, 547, 574, 745, 754, 448, 484, 844, 88, 79, 97, 6(10), (10)6, 5(11), (11)5, 4(12), (12)4, (16).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..170

Crossrefs

Cf. A011782, A103488, A332716, A332721, A332747.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1,
      add(b(n-j, k), j=k..n))
    end:
a:= n-> b(n^2, n):
seq(a(n), n=0..23);

Mathematica

b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - j, k], {j, k, n}]];
a[n_] := b[n^2, n];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Mar 04 2022, after Alois P. Heinz *)