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A035661
Number of partitions of n into parts 7k+1 and 7k+6 with at least one part of each type.
3
0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 4, 4, 4, 4, 4, 5, 7, 10, 11, 11, 11, 12, 14, 18, 23, 25, 26, 27, 29, 33, 40, 47, 52, 55, 58, 62, 70, 81, 93, 102, 109, 115, 124, 137, 155, 173, 190, 203, 216, 232, 255, 283, 313, 340, 365, 388, 417, 454, 499, 544, 590, 631, 674
OFFSET
1,13
LINKS
FORMULA
G.f. : (-1 + 1/Product_{k>=0} (1 - x^(7 k + 6)))*(-1 + 1/Product_{k>=0} (1 - x^(7 k + 1))). - Robert Price, Aug 14 2020
MATHEMATICA
nmax = 66; s1 = Range[0, nmax/7]*7 + 1; 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 14 2020 *)
nmax = 66; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 6)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 14 2020 *)
KEYWORD
nonn
STATUS
approved