A035661 Number of partitions of n into parts 7k+1 and 7k+6 with at least one part of each type.

0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 4, 4, 4, 4, 4, 5, 7, 10, 11, 11, 11, 12, 14, 18, 23, 25, 26, 27, 29, 33, 40, 47, 52, 55, 58, 62, 70, 81, 93, 102, 109, 115, 124, 137, 155, 173, 190, 203, 216, 232, 255, 283, 313, 340, 365, 388, 417, 454, 499, 544, 590, 631, 674

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^(7 k + 6)))*(-1 + 1/Product_{k>=0} (1 - x^(7 k + 1))). - Robert Price, Aug 14 2020

Mathematica

nmax = 66; s1 = Range[0, nmax/7]*7 + 1; s2 = Range[0, nmax/7]*7 + 6;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 14 2020 *)
nmax = 66; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 6)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 14 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035660, A035662-A035699.

Sequence in context: A035684 A049111 A096509 * A287393 A260085 A159461

Adjacent sequences: A035658 A035659 A035660 * A035662 A035663 A035664

Keyword

nonn

Author

Olivier Gérard

Status

approved