A035663 Number of partitions of n into parts 7k+2 and 7k+4 with at least one part of each type.

0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 3, 2, 3, 4, 4, 4, 7, 6, 9, 6, 13, 8, 15, 12, 19, 16, 21, 23, 25, 27, 32, 35, 40, 39, 53, 47, 63, 57, 78, 71, 88, 91, 104, 109, 121, 135, 146, 154, 179, 182, 213, 209, 257, 250, 295, 300, 344, 356, 392, 426, 459, 491, 539, 572, 633

Offset

1,10

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 125 terms from Robert Price)

Formula

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(7 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(7 k + 4))). - Robert Price, Aug 16 2020

Mathematica

nmax = 68; s1 = Range[0, nmax/7]*7 + 2; s2 = Range[0, nmax/7]*7 + 4;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 14 2020 *)
nmax = 68; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 4)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020 *)

Crossrefs

Cf. A035441-A035468, A035618-A035662, A035664-A035699.

Sequence in context: A262676 A070101 A022830 * A117192 A078729 A300236

Adjacent sequences: A035660 A035661 A035662 * A035664 A035665 A035666

Keyword

nonn

Author

Olivier Gérard

Status

approved