A035626 Number of partitions of n into parts 4k+2 and 4k+3 with at least one part of each type.

0, 0, 0, 0, 1, 0, 1, 1, 3, 1, 4, 3, 7, 4, 10, 8, 15, 11, 21, 18, 30, 24, 42, 37, 56, 50, 78, 70, 102, 95, 137, 129, 179, 171, 236, 227, 303, 297, 395, 386, 502, 501, 643, 641, 814, 820, 1030, 1041, 1291, 1317, 1622, 1652, 2018, 2075, 2509, 2582, 3107, 3212, 3834

Offset

1,9

Links

Alois P. Heinz, Table of n, a(n) for n = 1..5000 (first 100 terms from Robert Price)

Formula

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(4 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(4 k + 3))). - Robert Price, Aug 16 2020

Mathematica

nmax = 59; s1 = Range[0, nmax/4]*4 + 2; s2 = Range[0, nmax/4]*4 + 3;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 06 2020 *)
nmax = 59; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(4 k + 3)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(4 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020 *)

Crossrefs

Bisection of A035695 (even part).

Cf. A035441-A035468, A035618-A035625, A035627-A035699.

Sequence in context: A264596 A262214 A340760 * A082587 A364670 A060043

Adjacent sequences: A035623 A035624 A035625 * A035627 A035628 A035629

Keyword

nonn

Author

Olivier Gérard

Status

approved