A035644 Number of partitions of n into parts 6k+1 and 6k+4 with at least one part of each type.

0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 4, 4, 5, 5, 7, 7, 11, 12, 14, 14, 19, 20, 26, 28, 34, 35, 43, 45, 56, 61, 72, 75, 90, 96, 113, 122, 143, 151, 175, 186, 216, 233, 268, 284, 325, 348, 395, 424, 483, 515, 580, 619, 697, 748, 841, 897, 1002, 1072, 1193, 1277, 1425

Offset

1,9

Links

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

Formula

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(6 k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(6 k + 4))). - Robert Price, Aug 16 2020

Mathematica

nmax = 61; s1 = Range[0, nmax/6]*6 + 1; s2 = Range[0, nmax/6]*6 + 4;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 13 2020 *)
nmax = 61; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 4)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035643, A035645-A035699.

Sequence in context: A319398 A260734 A265428 * A288773 A288774 A113474

Adjacent sequences: A035641 A035642 A035643 * A035645 A035646 A035647

Keyword

nonn

Author

Olivier Gérard

Status

approved