login
A035628
Number of partitions of n into parts 5k and 5k+2 with at least one part of each type.
3
0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 3, 1, 3, 1, 3, 7, 3, 8, 3, 8, 14, 8, 17, 8, 18, 26, 18, 33, 18, 36, 47, 37, 61, 37, 68, 81, 71, 106, 72, 121, 138, 128, 181, 131, 209, 228, 224, 297, 231, 347, 372, 376, 482, 391, 566, 592, 619, 760, 648, 898, 934, 989, 1188, 1043
OFFSET
1,12
LINKS
FORMULA
G.f.: (-1 + 1/Product_{k>=0} (1-x^(5k+2)))*(-1 + 1/Product_{k>=1} (1-x^(5k))). - Robert Price, Aug 07 2020
MATHEMATICA
nmax = 65; s1 = Range[1, nmax/5]*5; s2 = Range[0, nmax/5]*5 + 2;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 06 2020 *)
nmax = 65; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 06 2020 *)
KEYWORD
nonn
STATUS
approved