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A339060
Number of compositions (ordered partitions) of n into distinct parts congruent to 3 mod 4.
7
1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 4, 1, 0, 6, 4, 1, 0, 6, 6, 1, 0, 12, 6, 1, 0, 18, 8, 1, 24, 24, 8, 1, 24, 30, 10, 1, 48, 42, 10, 1, 72, 48, 12, 1, 120, 60, 12, 121, 144, 72, 14, 121, 216, 84, 14, 241, 264, 96, 16, 361, 360, 114, 16, 601, 432, 126, 18, 841
OFFSET
0,11
FORMULA
G.f.: Sum_{k>=0} k! * x^(k*(2*k + 1)) / Product_{j=1..k} (1 - x^(4*j)).
EXAMPLE
a(21) = 6 because we have [11, 7, 3], [11, 3, 7], [7, 11, 3], [7, 3, 11], [3, 11, 7] and [3, 7, 11].
MATHEMATICA
nmax = 75; CoefficientList[Series[Sum[k! x^(k (2 k + 1))/Product[1 - x^(4 j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 22 2020
STATUS
approved