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A035692
Number of partitions of n into parts 8k+3 and 8k+6 with at least one part of each type.
3
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 3, 0, 4, 3, 3, 4, 4, 4, 6, 4, 8, 6, 9, 9, 8, 11, 13, 8, 19, 14, 15, 21, 18, 19, 30, 19, 32, 32, 29, 38, 41, 36, 53, 43, 56, 59, 59, 67, 75, 70, 93, 81, 102, 105, 105, 122, 133, 123, 165, 145, 170, 189, 183, 203, 237
OFFSET
1,15
LINKS
FORMULA
G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 3)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 6))). - Robert Price, Aug 15 2020
MATHEMATICA
nmax = 75; s1 = Range[0, nmax/8]*8 + 3; s2 = Range[0, nmax/8]*8 + 6;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 15 2020 *)
nmax = 75; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 3)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 6)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 15 2020*)
KEYWORD
nonn
STATUS
approved