A035648 Number of partitions of n into parts 6k+2 and 6k+5 with at least one part of each type.

0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 3, 1, 3, 1, 4, 3, 7, 3, 8, 4, 10, 8, 14, 9, 17, 11, 22, 17, 28, 20, 34, 25, 43, 35, 53, 42, 64, 51, 80, 67, 96, 80, 115, 98, 142, 123, 168, 147, 200, 178, 244, 217, 286, 257, 339, 310, 407, 371, 475, 439, 559, 523, 664, 618, 772, 726

Offset

1,13

Links

Alois P. Heinz, Table of n, a(n) for n = 1..5000 (first 100 terms from Robert Price)

Formula

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(6 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(6 k + 5))). - Robert Price, Aug 16 2020

Mathematica

nmax = 68; s1 = Range[0, nmax/6]*6 + 2; s2 = Range[0, nmax/6]*6 + 5;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 13 2020 *)
nmax = 68; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035647, A035649-A035699.

Sequence in context: A095660 A290080 A289617 * A369069 A322821 A213621

Adjacent sequences: A035645 A035646 A035647 * A035649 A035650 A035651

Keyword

nonn

Author

Olivier Gérard

Status

approved