A035652 Number of partitions of n into parts 7k and 7k+2 with at least one part of each type.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 3, 1, 3, 1, 3, 1, 3, 7, 3, 8, 3, 8, 3, 8, 14, 8, 17, 8, 18, 8, 18, 26, 18, 33, 18, 36, 18, 37, 47, 37, 61, 37, 68, 37, 71, 81, 72, 106, 72, 121, 72, 128, 138, 131, 181, 132, 209, 132, 224, 228, 231, 297, 234, 347, 235, 376, 373

Offset

1,16

Links

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

Formula

G.f. : (-1 + 1/Product_{k>=0} (1 - x^(7 k + 2)))*(-1 + 1/Product_{k>=1} (1 - x^(7 k))). - Robert Price, Aug 12 2020

Mathematica

nmax = 72; s1 = Range[1, nmax/7]*7; s2 = Range[0, nmax/7]*7 + 2;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 12 2020 *)
nmax = 72; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 12 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035651, A035653-A035699.

Sequence in context: A104740 A111736 A330889 * A359943 A362720 A205526

Adjacent sequences: A035649 A035650 A035651 * A035653 A035654 A035655

Keyword

nonn

Author

Olivier Gérard

Status

approved