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A035696 Number of partitions of n into parts 8k+4 and 8k+7 with at least one part of each type. 3
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 3, 0, 0, 1, 3, 0, 1, 3, 6, 0, 1, 3, 7, 1, 3, 7, 11, 1, 3, 8, 14, 3, 7, 14, 20, 3, 8, 17, 26, 7, 15, 27, 34, 8, 18, 34, 45, 15, 30, 48, 57, 18, 37, 61, 75, 31, 55, 83, 94, 38, 69, 106, 123, 58, 98, 139, 152, 72, 123, 177, 197, 105 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,19

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 + 4)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 7))). - Robert Price, Aug 16 2020

MATHEMATICA

nmax = 80; s1 = Range[0, nmax/8]*8 + 4; s2 = Range[0, nmax/8]*8 + 7;

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

x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 16 2020 *)

nmax = 80; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 4)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 7)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020*)

CROSSREFS

Cf. A035441-A035468, A035618-A035695, A035697-A035699.

Sequence in context: A280815 A165974 A090622 * A170840 A300725 A035630

Adjacent sequences:  A035693 A035694 A035695 * A035697 A035698 A035699

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified February 25 08:17 EST 2021. Contains 341596 sequences. (Running on oeis4.)