A035651 Number of partitions of n into parts 7k and 7k+1 with at least one part of each type.

0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 10, 11, 11, 11, 11, 11, 11, 22, 25, 26, 26, 26, 26, 26, 44, 51, 54, 55, 55, 55, 55, 84, 98, 105, 108, 109, 109, 109, 153, 178, 193, 200, 203, 204, 204, 270, 313, 341, 356, 363, 366, 367, 463, 532, 582, 611

Offset

1,15

Links

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

Formula

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

Mathematica

nmax = 67; s1 = Range[1, nmax/7]*7; s2 = Range[0, nmax/7]*7 + 1;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 12 2020 *)
nmax = 67; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 1)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 12 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035650, A035652-A035699.

Sequence in context: A113472 A105682 A049109 * A007208 A165919 A035637

Adjacent sequences: A035648 A035649 A035650 * A035652 A035653 A035654

Keyword

nonn

Author

Olivier Gérard

Status

approved