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A282583 Number of compositions (ordered partitions) of n into quarter-squares (A002620). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 19 18:31 EST 2018. Contains 299356 sequences. (Running on oeis4.)