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A035623 Number of partitions of n into parts 4k and 4k+3 with at least one part of each type 1
0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 3, 0, 1, 3, 6, 1, 3, 7, 12, 3, 7, 15, 21, 7, 16, 28, 36, 16, 31, 50, 60, 32, 57, 85, 98, 60, 100, 141, 157, 107, 169, 226, 248, 184, 276, 358, 385, 305, 442, 553, 591, 495, 691, 845, 896, 782, 1063, 1270, 1343, 1216, 1608, 1890, 1993 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,11

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

G.f.: (-1 + 1/Product_{k >=0} (1-x^(4k+3)))*(-1 + 1/Product_{k>=1} (1-x^(4k))). - Robert Israel, Feb 23 2016

a(n) ~ exp(Pi*sqrt(n/3)) * Pi^(3/4) / (2^(5/4) * 3^(5/8) * Gamma(1/4) * n^(9/8)). - Vaclav Kotesovec, May 26 2018

MAPLE

N:= 100:

P:= (-1 + 1/mul(1-x^(4*k+3), k=0..(N-3)/4))*(-1 + 1/mul(1-x^(4*k), k=1..N/4)):

S:= series(P, x, N+1):

seq(coeff(S, x, j), j=1..N); # Robert Israel, Feb 23 2016

CROSSREFS

Sequence in context: A091867 A127158 A112367 * A248949 A083857 A115142

Adjacent sequences:  A035620 A035621 A035622 * A035624 A035625 A035626

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified October 22 23:18 EDT 2018. Contains 316518 sequences. (Running on oeis4.)