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A035682
Number of partitions of n into parts 8k+1 and 8k+5 with at least one part of each type.
3
0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 4, 4, 5, 5, 5, 7, 7, 8, 11, 12, 14, 14, 15, 19, 20, 22, 26, 29, 34, 35, 37, 43, 46, 51, 57, 63, 72, 76, 81, 91, 98, 107, 117, 128, 144, 153, 163, 179, 192, 210, 226, 245, 272, 290, 310, 336, 360, 391, 418, 450, 494, 527, 564, 605
OFFSET
1,11
LINKS
FORMULA
G.f. : (-1 + 1/Product_{k>=0} (1 - x^(8 k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 5). - Robert Price, Aug 15 2020
MATHEMATICA
nmax = 67; s1 = Range[0, nmax/8]*8 + 1; 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 = 67; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 15 2020*)
KEYWORD
nonn
STATUS
approved