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A035687 Number of partitions of n into parts 8k+2 and 8k+5 with at least one part of each type. 4
0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 3, 1, 4, 1, 4, 3, 4, 4, 7, 4, 10, 4, 11, 8, 11, 11, 15, 12, 21, 12, 25, 18, 26, 24, 31, 28, 42, 29, 50, 38, 55, 50, 62, 58, 79, 63, 95, 76, 105, 96, 118, 113, 144, 123, 172, 145, 193, 178, 213, 208, 255, 230, 302, 262, 340, 316 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,15

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..5000

FORMULA

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 5))). - Robert Price, Aug 15 2020

MATHEMATICA

nmax = 70; s1 = Range[0, nmax/8]*8 + 2; s2 = Range[0, nmax/8]*8 + 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 = 70; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 15 2020*)

CROSSREFS

Cf. A035441-A035468, A035618-A035686, A035688-A035699.

Sequence in context: A294098 A087477 A029212 * A324542 A302792 A179820

Adjacent sequences:  A035684 A035685 A035686 * A035688 A035689 A035690

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified September 26 09:15 EDT 2021. Contains 347664 sequences. (Running on oeis4.)