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A035634
Number of partitions of n into parts 5k+2 and 5k+3 with at least one part of each type.
3
0, 0, 0, 0, 1, 0, 1, 1, 1, 3, 2, 3, 4, 4, 7, 6, 9, 10, 11, 16, 15, 20, 23, 25, 32, 34, 41, 47, 52, 63, 68, 80, 90, 101, 116, 129, 147, 166, 184, 210, 232, 262, 292, 326, 363, 405, 450, 501, 554, 617, 681, 756, 834, 924, 1015, 1125, 1235, 1363, 1498, 1647, 1809
OFFSET
1,10
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^(5 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(5 k + 3))). - Robert Price, Aug 16 2020
MATHEMATICA
nmax = 61; s1 = Range[0, nmax/5]*5 + 2; s2 = Range[0, nmax/5]*5 + 3;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 07 2020 *)
nmax = 61; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 16 2020 *)
KEYWORD
nonn
STATUS
approved