A282583 Number of compositions (ordered partitions) of n into quarter-squares (A002620).

1, 1, 2, 3, 6, 10, 19, 33, 60, 107, 193, 345, 621, 1113, 1999, 3586, 6439, 11554, 20741, 37223, 66814, 119916, 215237, 386310, 693375, 1244494, 2233686, 4009113, 7195757, 12915268, 23180946, 41606232, 74676840, 134033474, 240569601, 431785583, 774989076, 1390986741, 2496608365, 4481029864, 8042762869

Offset: 0

Author

Ilya Gutkovskiy, Feb 19 2017

Keywords

• nonn

Examples

			a(4) = 6 because we have [4], [2, 2], [2, 1, 1], [1, 2, 1], [1, 1, 2] and [1, 1, 1, 1].
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..200
• Index entries for sequences related to compositions

Crossrefs

Cf. A002620, A006456, A197081, A197122.

Programs

Mathematica

nmax = 40; CoefficientList[Series[1/(1 - Sum[x^Floor[k^2/4], {k, 2, nmax}]), {x, 0, nmax}], x]

PARI

Vec(1/(1 - sum(k=2, 40, x^floor(k^2/4)) + O(x^41))) \\ Indranil Ghosh, Mar 15 2017

Formula

G.f.: 1/(1 - Sum_{k>=2} x^(floor(k^2/4))).