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A035668
Number of partitions of n into parts 7k+3 and 7k+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, 2, 0, 2, 2, 0, 3, 4, 3, 3, 4, 4, 4, 6, 8, 8, 6, 9, 11, 8, 13, 18, 13, 14, 21, 19, 18, 29, 30, 25, 32, 38, 35, 40, 51, 52, 50, 59, 66, 67, 73, 89, 93, 89, 104, 119, 115, 129, 156, 154, 153, 186, 195, 195, 228, 254, 251, 269, 304, 319
OFFSET
1,15
LINKS
FORMULA
G.f. : (-1 + 1/Product_{k>=0} (1 - x^(7 k + 3)))*(-1 + 1/Product_{k>=0} (1 - x^(7 k + 6)). - Robert Price, Aug 15 2020
MATHEMATICA
nmax = 74; s1 = Range[0, nmax/7]*7 + 3; s2 = Range[0, nmax/7]*7 + 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 = 74; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 3)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 6)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 15 2020*)
KEYWORD
nonn
STATUS
approved