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A035669 Number of partitions of n into parts 7k+4 and 7k+5 with at least one part of each type. 3
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 2, 1, 1, 1, 2, 3, 1, 4, 3, 3, 3, 5, 7, 4, 7, 7, 8, 8, 10, 13, 10, 14, 15, 16, 17, 20, 25, 21, 26, 29, 32, 33, 37, 45, 41, 47, 54, 58, 61, 65, 79, 76, 83, 94, 103, 108, 113, 132, 135, 143, 160, 172, 185, 192, 219, 227, 240, 265, 286 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,16

LINKS

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

FORMULA

G.f. : (-1 + 1/Product_{k>=0} (1 - x^(7 k + 4)))*(-1 + 1/Product_{k>=0} (1 - x^(7 k + 5)). - Robert Price, Aug 15 2020

MATHEMATICA

nmax = 74; s1 = Range[0, nmax/7]*7 + 4; s2 = Range[0, nmax/7]*7 + 5;

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

x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 15 2020 *)

nmax = 74; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 4)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 15 2020*)

CROSSREFS

Cf. A035441-A035468, A035618-A035668, A035670-A035699.

Sequence in context: A249298 A088863 A053283 * A126863 A106806 A178526

Adjacent sequences:  A035666 A035667 A035668 * A035670 A035671 A035672

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified May 18 22:17 EDT 2021. Contains 344004 sequences. (Running on oeis4.)