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A035689
Number of partitions of n into parts 8k+2 and 8k+7 with at least one part of each type.
3
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 3, 1, 3, 1, 3, 1, 4, 3, 7, 3, 8, 3, 8, 4, 10, 8, 14, 9, 16, 9, 18, 11, 22, 17, 28, 19, 32, 21, 36, 25, 44, 35, 52, 40, 60, 44, 68, 52, 82, 66, 95, 76, 108, 85, 123, 100, 145, 122, 166, 140, 188, 157, 214, 182, 250, 215, 283, 245
OFFSET
1,17
LINKS
FORMULA
G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 7))). - Robert Price, Aug 15 2020
MATHEMATICA
nmax = 74; s1 = Range[0, nmax/8]*8 + 2; 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 15 2020 *)
nmax = 74; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 7)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 15 2020*)
KEYWORD
nonn
STATUS
approved