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A035660
Number of partitions of n into parts 7k+1 and 7k+5 with at least one part of each type.
3
0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 4, 4, 4, 5, 5, 7, 7, 10, 12, 12, 14, 14, 18, 20, 24, 28, 29, 33, 35, 41, 45, 51, 59, 63, 71, 75, 85, 94, 104, 118, 126, 140, 150, 166, 182, 198, 222, 239, 263, 282, 308, 337, 364, 403, 433, 473, 508, 550, 599, 643, 705, 758, 823, 884
OFFSET
1,11
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 + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(7 k + 5))). - Robert Price, Aug 16 2020
MATHEMATICA
nmax = 66; s1 = Range[0, nmax/7]*7 + 1; s2 = Range[0, nmax/7]*7 + 5;
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 + 5)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 16 2020 *)
KEYWORD
nonn
STATUS
approved