A035635 Number of partitions of n into parts 5k+2 and 5k+4 with at least one part of each type.

0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 3, 4, 6, 4, 8, 6, 12, 10, 14, 14, 18, 21, 25, 25, 33, 33, 46, 43, 56, 57, 71, 77, 88, 95, 113, 121, 146, 148, 180, 188, 224, 238, 271, 294, 336, 364, 416, 439, 509, 540, 621, 661, 744, 805, 902, 978, 1090, 1168, 1315, 1408, 1581

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^(5 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(5 k + 4))). - Robert Price, Aug 16 2020

Mathematica

nmax = 64;  s1 = Range[0, nmax/5]*5 + 2; s2 = Range[0, nmax/5]*5 + 4;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 07 2020 *)
nmax = 64; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 4)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035634, A035636-A035699.

Sequence in context: A238213 A193942 A098527 * A114869 A316899 A352828

Adjacent sequences: A035632 A035633 A035634 * A035636 A035637 A035638

Keyword

nonn

Author

Olivier Gérard

Status

approved