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A035648
Number of partitions of n into parts 6k+2 and 6k+5 with at least one part of each type.
3
0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 3, 1, 3, 1, 4, 3, 7, 3, 8, 4, 10, 8, 14, 9, 17, 11, 22, 17, 28, 20, 34, 25, 43, 35, 53, 42, 64, 51, 80, 67, 96, 80, 115, 98, 142, 123, 168, 147, 200, 178, 244, 217, 286, 257, 339, 310, 407, 371, 475, 439, 559, 523, 664, 618, 772, 726
OFFSET
1,13
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..5000 (first 100 terms from Robert Price)
FORMULA
G.f.: (-1 + 1/Product_{k>=0} (1 - x^(6 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(6 k + 5))). - Robert Price, Aug 16 2020
MATHEMATICA
nmax = 68; s1 = Range[0, nmax/6]*6 + 2; s2 = Range[0, nmax/6]*6 + 5;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 13 2020 *)
nmax = 68; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 16 2020 *)
KEYWORD
nonn
STATUS
approved