A138269 a(n+1) is the Hankel transform of C(n)+C(n+2), where C(n) = A000108(n).

1, 3, 12, 53, 231, 1000, 4329, 18747, 81188, 351597, 1522639, 6594000, 28556241, 123666803, 535556412, 2319302053, 10044062391, 43497219000, 188370799289, 815766130347, 3532789487188, 15299239691997

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (5,-4,5,-1).

Formula

G.f.: (1-x)^2/(1-5*x+4*x^2-5*x^3+x^4).

a(n) = Re(P(2n,i)*CONJ(P(2n+1,i))) where i=sqrt(-1) and P(n,x) = Sum_{k=0..floor(n/2)} binomial(n-k,k) x^k.

a(n) = 5*a(n-1)-4*a(n-2)+5*a(n-3)-a(n-4). - Wesley Ivan Hurt, Mar 07 2022

Mathematica

LinearRecurrence[{5, -4, 5, -1}, {1, 3, 12, 53}, 30] (* Harvey P. Dale, Dec 04 2022 *)

Crossrefs

Cf. A000108, A092886, A138268.

Sequence in context: A274396 A299113 A124202 * A228771 A370023 A151198

Adjacent sequences: A138266 A138267 A138268 * A138270 A138271 A138272

Keyword

easy,nonn

Author

Paul Barry, Mar 10 2008

Status

approved