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A035644 Number of partitions of n into parts 6k+1 and 6k+4 with at least one part of each type. 3
0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 4, 4, 5, 5, 7, 7, 11, 12, 14, 14, 19, 20, 26, 28, 34, 35, 43, 45, 56, 61, 72, 75, 90, 96, 113, 122, 143, 151, 175, 186, 216, 233, 268, 284, 325, 348, 395, 424, 483, 515, 580, 619, 697, 748, 841, 897, 1002, 1072, 1193, 1277, 1425 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

LINKS

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

FORMULA

G.f.: (-1 + 1/Product_{k>=0} (1 - x^(6 k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(6 k + 4))). - Robert Price, Aug 16 2020

MATHEMATICA

nmax = 61; s1 = Range[0, nmax/6]*6 + 1; s2 = Range[0, nmax/6]*6 + 4;

Table[Count[IntegerPartitions[n, All, s1~Join~s2],

x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 13 2020 *)

nmax = 61; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 4)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020 *)

CROSSREFS

Cf. A035441-A035468, A035618-A035643, A035645-A035699.

Sequence in context: A319398 A260734 A265428 * A288773 A288774 A113474

Adjacent sequences:  A035641 A035642 A035643 * A035645 A035646 A035647

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified November 25 05:43 EST 2020. Contains 338617 sequences. (Running on oeis4.)