A035686 Number of partitions of n into parts 8k+2 and 8k+4 with at least one part of each type.

0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 5, 0, 5, 0, 8, 0, 8, 0, 14, 0, 15, 0, 22, 0, 23, 0, 34, 0, 37, 0, 51, 0, 54, 0, 74, 0, 81, 0, 107, 0, 116, 0, 150, 0, 165, 0, 210, 0, 229, 0, 287, 0, 316, 0, 392, 0, 430, 0, 526, 0, 580, 0, 704, 0, 774, 0, 929, 0, 1024, 0, 1223, 0, 1347, 0

Offset

1,10

Links

Robert Price, Table of n, a(n) for n = 1..1000

Formula

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 4))). - Robert Price, Aug 15 2020

Mathematica

nmax = 77; s1 = Range[0, nmax/8]*8 + 2; s2 = Range[0, nmax/8]*8 + 4;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 15 2020 *)
nmax = 77; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 4)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 15 2020*)

Crossrefs

Cf. A035441-A035468, A035618-A035685, A035687-A035699.

Sequence in context: A067770 A079200 A011420 * A308214 A327371 A037228

Adjacent sequences: A035683 A035684 A035685 * A035687 A035688 A035689

Keyword

nonn

Author

Olivier Gérard

Status

approved