A035628 Number of partitions of n into parts 5k and 5k+2 with at least one part of each type.

0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 3, 1, 3, 1, 3, 7, 3, 8, 3, 8, 14, 8, 17, 8, 18, 26, 18, 33, 18, 36, 47, 37, 61, 37, 68, 81, 71, 106, 72, 121, 138, 128, 181, 131, 209, 228, 224, 297, 231, 347, 372, 376, 482, 391, 566, 592, 619, 760, 648, 898, 934, 989, 1188, 1043

Offset

1,12

Links

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

Formula

G.f.: (-1 + 1/Product_{k>=0} (1-x^(5k+2)))*(-1 + 1/Product_{k>=1} (1-x^(5k))). - Robert Price, Aug 07 2020

Mathematica

nmax = 65; s1 = Range[1, nmax/5]*5; s2 = Range[0, nmax/5]*5 + 2;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 06 2020 *)
nmax = 65; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 06 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035627, A035629-A035699.

Sequence in context: A185091 A332031 A023511 * A187562 A370719 A057024

Adjacent sequences: A035625 A035626 A035627 * A035629 A035630 A035631

Keyword

nonn

Author

Olivier Gérard

Status

approved