login
A035637
Number of partitions of n into parts 6k and 6k+1 with at least one part of each type.
3
0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 10, 11, 11, 11, 11, 11, 22, 25, 26, 26, 26, 26, 44, 51, 54, 55, 55, 55, 84, 98, 105, 108, 109, 109, 153, 178, 193, 200, 203, 204, 270, 313, 341, 356, 363, 366, 463, 532, 582, 611, 626, 633, 774, 884, 968, 1021
OFFSET
1,13
LINKS
FORMULA
G.f.: (-1 + 1/Product_{k>=0} (1-x^(6k+1)))*(-1 + 1/Product_{k>=1} (1-x^(6k))). - Robert Price, Aug 07 2020
MATHEMATICA
nmax = 64; s1 = Range[1, nmax/6]*6; s2 = Range[0, nmax/6]*6 + 1;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 07 2020 *)
nmax = 64; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 1)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 07 2020 *)
KEYWORD
nonn
STATUS
approved