A333048 Number of compositions of n^2 into powers of n.

1, 1, 6, 20, 96, 572, 3971, 31201, 272334, 2605268, 27042522, 302171806, 3611295430, 45911641817, 618074912240, 8776287336812, 130994094465946, 2049114914257540, 33504826964461451, 571285301051283841, 10136481840545237652, 186803012671904648805

Offset: 0

Author

Alois P. Heinz, Mar 06 2020

Keywords

• nonn

Examples

			a(0) = 1: the empty composition.
a(1) = 1: 1.
a(2) = 6: 1111, 112, 121, 211, 22, 4.
a(3) = 20: 111111111, 1111113, 1111131, 1111311, 1113111, 1131111, 1311111, 3111111, 11133, 11313, 11331, 13113, 13131, 13311, 31113, 31131, 31311, 33111, 333, 9.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A000290, A011782, A103488, A332721, A332747, A332796.

Programs

Maple

a:= n-> `if`(n<2, 1, 1+add(binomial(n*(n-j)+j, j), j=0..n)):
seq(a(n), n=0..21);

Formula

a(n) = 1 + Sum_{j=0..n} binomial(n*(n-j)+j,j) if n>1, a(0) = a(1) = 1.