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

0,7

Links

Table of n, a(n) for n=0..70.

Index entries for sequences related to compositions

Formula

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

Example

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].

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]

Crossrefs

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

Sequence in context: A112171 A112172 A093085 * A023555 A357704 A294203

Adjacent sequences: A339056 A339057 A339058 * A339060 A339061 A339062

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 22 2020

Status

approved