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A035651
Number of partitions of n into parts 7k and 7k+1 with at least one part of each type.
3
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 10, 11, 11, 11, 11, 11, 11, 22, 25, 26, 26, 26, 26, 26, 44, 51, 54, 55, 55, 55, 55, 84, 98, 105, 108, 109, 109, 109, 153, 178, 193, 200, 203, 204, 204, 270, 313, 341, 356, 363, 366, 367, 463, 532, 582, 611
OFFSET
1,15
LINKS
FORMULA
G.f. : (-1 + 1/Product_{k>=0} (1 - x^(7 k + 1)))*(-1 + 1/Product_{k>=1} (1 - x^(7 k))). - Robert Price, Aug 12 2020
MATHEMATICA
nmax = 67; s1 = Range[1, nmax/7]*7; s2 = Range[0, nmax/7]*7 + 1;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 12 2020 *)
nmax = 67; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 1)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 12 2020 *)
KEYWORD
nonn
STATUS
approved