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

0,3

Links

Indranil Ghosh, Table of n, a(n) for n = 0..200

Index entries for sequences related to compositions

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A002620, A006456, A197081, A197122.

Sequence in context: A007473 A014595 A079959 * A028495 A136752 A093126

Adjacent sequences: A282580 A282581 A282582 * A282584 A282585 A282586

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 19 2017

Status

approved