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

0,3

Links

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

Formula

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

Example

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.

Maple

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

Crossrefs

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

Sequence in context: A246036 A151485 A191424 * A200538 A238118 A211953

Adjacent sequences: A333045 A333046 A333047 * A333049 A333050 A333051

Keyword

nonn

Author

Alois P. Heinz, Mar 06 2020

Status

approved