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A035627 Number of partitions of n into parts 5k and 5k+1 with at least one part of each type. 3
0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 10, 11, 11, 11, 11, 22, 25, 26, 26, 26, 44, 51, 54, 55, 55, 84, 98, 105, 108, 109, 153, 178, 193, 200, 203, 270, 313, 341, 356, 363, 462, 532, 582, 611, 626, 771, 883, 968, 1021, 1050, 1259, 1431, 1571, 1663, 1717, 2017 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,11
LINKS
FORMULA
G.f.: (-1 + 1/Product_{k>=1} (1 - x^(5 k)))*(-1 + 1/Product_{k>=0} (1 - x^(5 k + 1))). - Robert Price, Aug 16 2020
MATHEMATICA
nmax = 61; s1 = Range[1, nmax/5]*5; s2 = Range[0, nmax/5]*5 + 1;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 06 2020 *)
nmax = 61; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 1)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 06 2020 *)
CROSSREFS
Sequence in context: A262690 A048760 A287392 * A228423 A165923 A228729
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)