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A035646 Number of partitions of n into parts 6k+2 and 6k+3 with at least one part of each type. 3
0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 4, 1, 4, 4, 4, 4, 10, 4, 11, 11, 11, 12, 22, 12, 25, 25, 26, 28, 45, 29, 52, 52, 55, 60, 87, 63, 101, 102, 108, 118, 160, 126, 187, 189, 202, 221, 285, 238, 333, 338, 363, 395, 492, 430, 574, 585, 629, 684, 828, 749, 964, 987, 1061 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,11
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..5000 (first 100 terms from Robert Price)
FORMULA
G.f.: (-1 + 1/Product_{k>=0} (1 - x^(6 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(6 k + 3))). - Robert Price, Aug 16 2020
MATHEMATICA
nmax = 63; s1 = Range[0, nmax/6]*6 + 2; s2 = Range[0, nmax/6]*6 + 3;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 13 2020 *)
nmax = 63; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 16 2020 *)
CROSSREFS
Sequence in context: A117445 A145079 A196222 * A144034 A366887 A204714
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)