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A035620
Number of partitions of n into parts 3k+1 and 3k+2 with at least one part of each type.
4
0, 0, 1, 1, 2, 4, 5, 7, 11, 14, 19, 26, 33, 43, 55, 70, 88, 111, 137, 170, 208, 256, 311, 378, 456, 551, 658, 790, 940, 1119, 1325, 1570, 1847, 2179, 2554, 2996, 3499, 4088, 4753, 5533, 6414, 7436, 8593, 9931, 11439, 13180, 15140, 17391, 19926, 22827
OFFSET
1,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 80 terms from Robert Price)
FORMULA
G.f.: (-1 + 1/Product_{k>=0} (1 - x^(3 k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(3 k + 2))). - Robert Price, Aug 16 2020
MATHEMATICA
nmax = 50; s1 = Range[0, nmax/3]*3 + 1; s2 = Range[0, nmax/3]*3 + 2;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 06 2020 *)
nmax = 50; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(3 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(3 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 16 2020*)
KEYWORD
nonn
STATUS
approved