A114878 a(n) = (1/15)*(3*Fibonacci(5*(n+1)) - 5*Fibonacci(4*(n+1))).

0, 4, 74, 1024, 12750, 150952, 1739556, 19740728, 222003850, 2483142420, 27682969578, 307999242192, 3422552275480, 38003214330588, 421781012676970, 4679808933074296, 51914858228808470, 575847287536870136

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..900

Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics 36(2), 2007, pp. 251-257. MR2312537. Zbl 1133.11012.

Index entries for linear recurrences with constant coefficients, signature (18,-77,4,1).

Formula

a(n) = Fibonacci(5*(n+1))/Fibonacci(5) - Fibonacci(4*(n+1))/Fibonacci(4).

Lim_{n -> oo} a(n+1)/a(n) = (1 + sqrt(5))^2*(2 + sqrt(5))/2.

G.f.: 2*x*(x+2)/((1 -7*x +x^2)*(1 -11*x -x^2)). - Colin Barker, Dec 10 2012

Mathematica

a[n_] := (1/15)*(3*Fibonacci[5*(n+1)] - 5*Fibonacci[4*(n+1)]);
Table[a[n], {n, 0, 30}] (* modified by G. C. Greubel, Jul 09 2021 *)

Prog

(Magma) [(3*Fibonacci(5*(n+1)) - 5*Fibonacci(4*(n+1)))/15: n in [0..30]]; // G. C. Greubel, Jul 09 2021
(Sage) [(3*fibonacci(5*(n+1)) - 5*fibonacci(4*(n+1)))/15 for n in (0..30)] # G. C. Greubel, Jul 09 2021

Crossrefs

Cf. A000045.

Sequence in context: A104335 A156494 A232371 * A368353 A131359 A108808

Adjacent sequences: A114875 A114876 A114877 * A114879 A114880 A114881

Keyword

easy,nonn

Author

Roger L. Bagula, Feb 20 2006

Extensions

Edited by G. C. Greubel, Jul 09 2021

Status

approved