A339088 Number of compositions (ordered partitions) of n into distinct parts congruent to 1 mod 6.

1, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 4, 6, 0, 0, 0, 1, 4, 6, 0, 0, 0, 1, 6, 12, 0, 0, 0, 1, 6, 18, 24, 0, 0, 1, 8, 24, 24, 0, 0, 1, 8, 30, 48, 0, 0, 1, 10, 42, 72, 0, 0, 1, 10, 48, 120, 120, 0, 1, 12, 60, 144, 120, 0, 1, 12, 72, 216, 240, 0, 1, 14, 84, 264, 360

Offset: 0

Author

Ilya Gutkovskiy, Nov 23 2020

Keywords

• nonn

Examples

			a(21) = 6 because we have [13, 7, 1], [13, 1, 7], [7, 13, 1], [7, 1, 13], [1, 13, 7] and [1, 7, 13].
		

Links

• Index entries for sequences related to compositions

Crossrefs

Cf. A005708, A016921, A032020, A032021, A109701, A280456, A337547, A337548, A339059, A339060, A339086, A339087, A339089.

Programs

Mathematica

nmax = 83; CoefficientList[Series[Sum[k! x^(k (3 k - 2))/Product[1 - x^(6 j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=0} k! * x^(k*(3*k - 2)) / Product_{j=1..k} (1 - x^(6*j)).