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A035663
Number of partitions of n into parts 7k+2 and 7k+4 with at least one part of each type.
3
0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 3, 2, 3, 4, 4, 4, 7, 6, 9, 6, 13, 8, 15, 12, 19, 16, 21, 23, 25, 27, 32, 35, 40, 39, 53, 47, 63, 57, 78, 71, 88, 91, 104, 109, 121, 135, 146, 154, 179, 182, 213, 209, 257, 250, 295, 300, 344, 356, 392, 426, 459, 491, 539, 572, 633
OFFSET
1,10
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 125 terms from Robert Price)
FORMULA
G.f.: (-1 + 1/Product_{k>=0} (1 - x^(7 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(7 k + 4))). - Robert Price, Aug 16 2020
MATHEMATICA
nmax = 68; s1 = Range[0, nmax/7]*7 + 2; s2 = Range[0, nmax/7]*7 + 4;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 14 2020 *)
nmax = 68; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 4)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 16 2020 *)
KEYWORD
nonn
STATUS
approved