A392074 a(n) = Sum_{k=0..floor(n/3)} 2^k * 3^(n-3*k) * binomial(k,4*(n-3*k)).

1, 0, 0, 2, 0, 0, 4, 0, 0, 8, 0, 0, 16, 48, 0, 32, 480, 0, 64, 2880, 0, 128, 13440, 0, 256, 53760, 2304, 512, 193536, 41472, 1024, 645120, 414720, 2048, 2027520, 3041280, 4096, 6082560, 18247680, 118784, 17571840, 94887936, 2891776, 49201152, 442810368, 40288256, 134184960, 1897758720

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,8,0,0,-24,0,0,32,0,0,-16,48).

Formula

G.f.: (1-2*x^3)^3 / ((1-2*x^3)^4 - 48*x^13).

a(n) = 8*a(n-3) - 24*a(n-6) + 32*a(n-9) - 16*a(n-12) + 48*a(n-13).

Mathematica

CoefficientList[Series[(1-2*x^3)^3/((1-2*x^3)^4-48*x^13), {x, 0, 50}], x] (* Vincenzo Librandi, Dec 31 2025 *)

Prog

(PARI) a178619(n, k) = sum(j=0, k, (-1)^(k-j)*binomial(n+1, k-j)*binomial(n+4*j, 4*j));
my(A=2, B=3, C=A^4*B, N=1, M=50, x='x+O('x^M), X=1-A*x^3, Y=13); Vec(sum(k=0, (3*N)\4, C^k*a178619(N-1, k)*X^(3*N-4*k)*x^(Y*k))/(X^4-C*x^Y)^N)
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1-2*x^3)^3 / ((1-2*x^3)^4 - 48*x^13)); // Vincenzo Librandi, Dec 31 2025

Crossrefs

Cf. A178619, A392042.

Sequence in context: A028601 A077958 A077959 * A022002 A392042 A084658

Adjacent sequences: A392071 A392072 A392073 * A392075 A392076 A392077

Keyword

nonn

Author

Seiichi Manyama, Dec 30 2025

Status

approved