A035632 Number of partitions of n into parts 5k+1 and 5k+3 with at least one part of each type.

0, 0, 0, 1, 1, 1, 2, 2, 4, 5, 5, 7, 8, 11, 14, 15, 19, 22, 27, 33, 37, 44, 50, 59, 71, 79, 93, 106, 120, 142, 159, 181, 207, 232, 267, 301, 339, 383, 428, 486, 544, 609, 683, 758, 853, 951, 1056, 1180, 1304, 1453, 1616, 1785, 1980, 2185, 2417, 2674, 2947, 3253

Offset

1,7

Links

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

Formula

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(5 k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(5 k + 3))). - Robert Price, Aug 16 2020

Mathematica

nmax = 58; s1 = Range[0, nmax/5]*5 + 1; s2 = Range[0, nmax/5]*5 + 3;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 07 2020 *)
nmax = 58; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035631, A035633-A035699.

Sequence in context: A159296 A277191 A335129 * A114701 A349464 A325260

Adjacent sequences: A035629 A035630 A035631 * A035633 A035634 A035635

Keyword

nonn

Author

Olivier Gérard

Status

approved