A035660 Number of partitions of n into parts 7k+1 and 7k+5 with at least one part of each type.

0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 4, 4, 4, 5, 5, 7, 7, 10, 12, 12, 14, 14, 18, 20, 24, 28, 29, 33, 35, 41, 45, 51, 59, 63, 71, 75, 85, 94, 104, 118, 126, 140, 150, 166, 182, 198, 222, 239, 263, 282, 308, 337, 364, 403, 433, 473, 508, 550, 599, 643, 705, 758, 823, 884

Offset

1,11

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 + 5))). - Robert Price, Aug 16 2020

Mathematica

nmax = 66; s1 = Range[0, nmax/7]*7 + 1; 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 14 2020 *)
nmax = 66; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035659, A035661-A035699.

Sequence in context: A101656 A090557 A230875 * A302405 A115367 A084841

Adjacent sequences: A035657 A035658 A035659 * A035661 A035662 A035663

Keyword

nonn

Author

Olivier Gérard

Status

approved