A035659 - OEIS

A035659

Number of partitions of n into parts 7k+1 and 7k+4 with at least one part of each type.

0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 4, 5, 5, 5, 7, 8, 8, 11, 14, 15, 15, 19, 22, 23, 27, 33, 37, 38, 44, 50, 54, 60, 71, 79, 84, 94, 106, 114, 125, 143, 159, 169, 187, 208, 225, 242, 273, 302, 323, 351, 390, 421, 451, 498, 551, 590, 636, 697, 757, 807, 881, 965, 1039

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OFFSET

1,9

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 125 terms from Robert Price)

FORMULA

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

MATHEMATICA

nmax = 64; s1 = Range[0, nmax/7]*7 + 1; s2 = Range[0, nmax/7]*7 + 4;

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

x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 14 2020 *)

nmax = 64; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 4)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 16 2020 *)

CROSSREFS

Cf. A035441-A035468, A035618-A035658, A035660-A035699.

Sequence in context: A035002 A032578 A351976 * A008282 A296690 A074765

Adjacent sequences: A035656 A035657 A035658 * A035660 A035661 A035662

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved