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A339089
Number of compositions (ordered partitions) of n into distinct parts congruent to 5 mod 6.
3
1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 4, 1, 0, 0, 0, 6, 4, 1, 0, 0, 0, 6, 6, 1, 0, 0, 0, 12, 6, 1, 0, 0, 0, 18, 8, 1, 0, 0, 24, 24, 8, 1, 0, 0, 24, 30, 10, 1, 0, 0, 48, 42, 10, 1, 0, 0, 72, 48, 12, 1, 0, 0, 120, 60, 12, 1, 0, 120, 144
OFFSET
0,17
FORMULA
G.f.: Sum_{k>=0} k! * x^(k*(3*k + 2)) / Product_{j=1..k} (1 - x^(6*j)).
EXAMPLE
a(33) = 6 because we have [17, 11, 5], [17, 5, 11], [11, 17, 5], [11, 5, 17], [5, 17, 11] and [5, 11, 17].
MATHEMATICA
nmax = 86; CoefficientList[Series[Sum[k! x^(k (3 k + 2))/Product[1 - x^(6 j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 23 2020
STATUS
approved