A339059 Number of compositions (ordered partitions) of n into distinct parts congruent to 1 mod 4.

1, 1, 0, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 4, 6, 0, 1, 4, 6, 0, 1, 6, 12, 0, 1, 6, 18, 24, 1, 8, 24, 24, 1, 8, 30, 48, 1, 10, 42, 72, 1, 10, 48, 120, 121, 12, 60, 144, 121, 12, 72, 216, 241, 14, 84, 264, 361, 14, 96, 360, 601, 16, 114, 432, 841, 736, 126, 552, 1201, 738

Offset: 0

Author

Ilya Gutkovskiy, Nov 22 2020

Keywords

• nonn

Examples

			a(15) = 6 because we have [9, 5, 1], [9, 1, 5], [5, 9, 1], [5, 1, 9], [1, 9, 5] and [1, 5, 9].
		

Links

• Index entries for sequences related to compositions

Crossrefs

Cf. A003269, A016813, A032020, A032021, A035451, A169975, A337547, A337548, A339060.

Programs

Mathematica

nmax = 70; CoefficientList[Series[Sum[k! x^(k (2 k - 1))/Product[1 - x^(4 j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=0} k! * x^(k*(2*k - 1)) / Product_{j=1..k} (1 - x^(4*j)).