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A035698 Number of partitions of n into parts 8k+5 and 8k+7 with at least one part of each type. 3
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 3, 3, 1, 2, 1, 3, 5, 3, 6, 5, 3, 5, 3, 8, 9, 7, 11, 8, 8, 10, 9, 15, 16, 15, 19, 15, 16, 20, 19, 28, 28, 27, 33, 27, 32, 36, 36, 48, 48, 49, 55, 48, 57, 64, 65, 82, 79, 83, 92, 83, 100, 106, 112, 134, 129 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,20
LINKS
FORMULA
G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 5)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 7))). - Robert Price, Aug 16 2020
MATHEMATICA
nmax = 81; s1 = Range[0, nmax/8]*8 + 5; s2 = Range[0, nmax/8]*8 + 7;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 16 2020 *)
nmax = 81; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 5)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 7)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 16 2020*)
CROSSREFS
Sequence in context: A190483 A090239 A165276 * A230204 A325592 A161502
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified April 22 07:37 EDT 2024. Contains 371892 sequences. (Running on oeis4.)