A391083 Expansion of g^2/(1 - x^3*g^4), where g = 1+x*g^4 is the g.f. of A002293.

1, 2, 9, 53, 346, 2433, 17983, 137725, 1083277, 8699016, 71023821, 587803305, 4920081835, 41578591148, 354267242982, 3040054009930, 26250340422636, 227915688825195, 1988540155710447, 17425785881358797, 153305830784509987, 1353538936713192275

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{k=0..floor(n/3)} (2*k+1) * binomial(4*n-8*k+2,n-3*k)/(2*n-4*k+1).

Mathematica

Table[Sum[ (2*k+1)*Binomial[4*n-8*k+2, n-3*k]/(2*n-4*k+1), {k, 0, Floor[n/3]}], {n, 0, 26}] (* Vincenzo Librandi, Nov 29 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (2*k+1)*binomial(4*n-8*k+2, n-3*k)/(2*n-4*k+1));
(Magma) [&+[(2*k+1)*Binomial(4*n-8*k+2, n-3*k)/(2*n-4*k+1): k in [0..Floor(n/3)]] : n in [0..40] ]; // Vincenzo Librandi, Nov 29 2025

Crossrefs

Cf. A389653, A391079, A391081.

Cf. A002293.

Sequence in context: A389653 A391079 A391081 * A074602 A394148 A379209

Adjacent sequences: A391080 A391081 A391082 * A391084 A391085 A391086

Keyword

nonn

Author

Seiichi Manyama, Nov 27 2025

Status

approved