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A035691 Number of partitions of n into parts 8k+3 and 8k+5 with at least one part of each type. 4
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 3, 1, 1, 3, 1, 3, 3, 2, 6, 3, 4, 7, 4, 8, 7, 6, 13, 8, 10, 15, 10, 17, 17, 14, 24, 19, 22, 30, 23, 33, 34, 31, 46, 39, 44, 56, 47, 63, 65, 61, 82, 75, 84, 101, 90, 113, 118, 115, 145, 137, 151, 176, 165, 197, 207, 206, 246, 242, 264 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,16
LINKS
FORMULA
G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 3)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 5))). - Robert Price, Aug 15 2020
MATHEMATICA
nmax = 74; s1 = Range[0, nmax/8]*8 + 3; s2 = Range[0, nmax/8]*8 + 5;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 15 2020 *)
nmax = 74; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 3)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 15 2020*)
CROSSREFS
Sequence in context: A131779 A131775 A218825 * A131781 A082465 A226856
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified February 21 08:45 EST 2024. Contains 370228 sequences. (Running on oeis4.)