A035683 Number of partitions of n into parts 8k+1 and 8k+6 with at least one part of each type.

0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 4, 4, 4, 4, 5, 5, 7, 7, 10, 11, 12, 12, 14, 14, 18, 19, 24, 26, 29, 29, 33, 34, 41, 43, 51, 55, 61, 63, 71, 73, 85, 90, 102, 110, 122, 126, 141, 146, 164, 174, 194, 207, 230, 239, 263, 275, 304, 322, 355, 377, 414, 433, 473, 495

Offset

1,13

Links

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

Formula

G.f. : (-1 + 1/Product_{k>=0} (1 - x^(8 k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 6). - Robert Price, Aug 15 2020

Mathematica

nmax = 68; s1 = Range[0, nmax/8]*8 + 1; s2 = Range[0, nmax/8]*8 + 6;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 15 2020 *)
nmax = 68; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 6)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 15 2020*)

Crossrefs

Cf. A035441-A035468, A035618-A035682, A035684-A035699.

Sequence in context: A083551 A080374 A165040 * A261009 A239896 A001670

Adjacent sequences: A035680 A035681 A035682 * A035684 A035685 A035686

Keyword

nonn

Author

Olivier Gérard

Status

approved