A390830 a(n) = Sum_{k=0..floor(n/4)} 2^k * 3^(n-3*k) * binomial(n-2*k,k) * binomial(n-3*k,k).

1, 3, 9, 27, 93, 351, 1377, 5427, 21357, 84159, 333153, 1326051, 5303421, 21289311, 85705857, 345845619, 1398456333, 5665268223, 22988910753, 93426350211, 380195618589, 1549080017055, 6318592156737, 25799086012563, 105436076580909, 431263713923775, 1765374618535137

Offset

0,2

Links

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

Formula

G.f.: 1 / sqrt((1-3*x)^2 - 24*x^4).

Mathematica

CoefficientList[Series[1/Sqrt[(1-3*x)^2-24*x^4], {x, 0, 30}], x] (* Vincenzo Librandi, Jan 04 2026 *)

Prog

(PARI) a098473(n, k) = binomial(n, k)*binomial(2*k, k);
my(A=2, B=3, C=A*B, N=0, M=30, x='x+O('x^M), X=1-B*x, Y=4); Vec(sum(k=0, N, (-C)^k*a098473(N, k)*X^(2*N-2*k)*x^(Y*k))/(X^2-4*C*x^Y)^(N+1/2))
(Magma) R<x> := PowerSeriesRing(Rationals(), 31); f := 1/Sqrt((1 - 3*x)^2 - 24*x^4); Coefficients(f); // Vincenzo Librandi, Jan 04 2026

Crossrefs

Cf. A391985, A391986.

Cf. A098473, A098482.

Sequence in context: A328080 A148925 A148926 * A146573 A148927 A148928

Adjacent sequences: A390827 A390828 A390829 * A390831 A390832 A390833

Keyword

nonn

Author

Seiichi Manyama, Dec 26 2025

Status

approved