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A035655 Number of partitions of n into parts 7k and 7k+5 with at least one part of each type. 3
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 3, 0, 0, 1, 0, 3, 0, 6, 1, 0, 3, 0, 7, 1, 11, 3, 0, 7, 1, 14, 3, 18, 7, 1, 15, 3, 25, 7, 30, 15, 3, 28, 7, 44, 15, 47, 29, 7, 51, 15, 72, 29, 73, 54, 15, 87, 29, 116, 55, 111, 94, 29, 144, 55, 180, 97, 167, 159, 55, 230, 98, 276 (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^(7 k + 5)))*(-1 + 1/Product_{k>=1} (1 - x^(7 k))). - Robert Price, Aug 12 2020

MATHEMATICA

nmax = 80; s1 = Range[1, nmax/7]*7; 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 12 2020 *)

nmax = 80; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 12 2020 *)

CROSSREFS

Cf. A035441-A035468, A035618-A035654, A035656-A035699.

Sequence in context: A331509 A171913 A074936 * A239446 A036857 A318508

Adjacent sequences:  A035652 A035653 A035654 * A035656 A035657 A035658

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified December 4 21:58 EST 2020. Contains 338941 sequences. (Running on oeis4.)