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A035674 Number of partitions of n into parts 8k and 8k+3 with at least one part of each type. 4
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 3, 1, 0, 3, 1, 0, 3, 1, 6, 3, 1, 7, 3, 1, 7, 3, 12, 7, 3, 15, 7, 3, 16, 7, 21, 16, 7, 28, 16, 7, 31, 16, 36, 32, 16, 50, 32, 16, 57, 32, 60, 60, 32, 85, 61, 32, 100, 61, 98, 107, 61, 141, 110, 61, 169, 111, 157, 184, 111, 226 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,19

LINKS

Robert Price, Table of n, a(n) for n = 1..1000

FORMULA

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8*k + 3)))*(-1 + 1/Product_{k>=1} (1 - x^(8*k))). - Robert Price, Aug 12 2020

MATHEMATICA

nmax = 78; s1 = Range[1, nmax/8]*8; s2 = Range[0, nmax/8]*8 + 3;

Table[Count[IntegerPartitions[n, All, s1~Join~s2],

x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 12 2020 *)

nmax = 78; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 12 2020 *)

CROSSREFS

Cf. A035441-A035468, A035618-A035673, A035675-A035699.

Sequence in context: A163972 A068464 A244679 * A058600 A133704 A160019

Adjacent sequences:  A035671 A035672 A035673 * A035675 A035676 A035677

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified June 24 18:38 EDT 2021. Contains 345419 sequences. (Running on oeis4.)