A120719 Expansion of 2*x^2*(305-727*x-315*x^2+60*x^3)/((1-x)*(1-7*x+x^2)*(1+3*x+x^2)).

0, 610, 1596, 16500, 97410, 707560, 4744080, 32791746, 224035980, 1537454500, 10532923170, 72206679000, 494878036896, 3392033285410, 23249109634140, 159352376426580, 1092215843858370, 7486162932788296, 51310913160533040

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,15,-15,-5,1).

Formula

G.f.: 2*x^2*(305-727*x-315*x^2+60*x^3)/((1-x)*(1-7*x+x^2)*(1+3*x+x^2)). - Colin Barker, Nov 01 2012

a(n) = -120*[n=0] + (2/25)*(677 + (2/3)*(37*Fibonacci(4*n+4) + 28*Fibonacci(4*n)) + (-1)^n*(749*Fibonacci(2*n+2) - 996*Fibonacci(2*n))). - G. C. Greubel, Jul 20 2023

Mathematica

LinearRecurrence[{5, 15, -15, -5, 1}, {0, 610, 1596, 16500, 97410}, 40] (* G. C. Greubel, Jul 20 2023 *)

Prog

(Magma)
F:=Fibonacci;
A120719:= func< n | (2/25)*(677 +(2/3)*(37*F(4*n+4) +28*F(4*n)) +(-1)^n*(749*F(2*n+2) -996*F(2*n))) >;
[A120719(n): n in [1..40]]; // G. C. Greubel, Jul 20 2023
(SageMath)
F=fibonacci
def A120719(n): return (2/25)*(677 +(2/3)*(37*F(4*n+4) +28*F(4*n)) +(-1)^n*(749*F(2*n+2) -996*F(2*n)))
[A120719(n) for n in range(1, 41)] # G. C. Greubel, Jul 20 2023

Crossrefs

Cf. A001906, A004187.

Sequence in context: A301561 A204487 A090177 * A045730 A072317 A220568

Adjacent sequences: A120716 A120717 A120718 * A120720 A120721 A120722

Keyword

nonn,easy

Author

Roger L. Bagula, Aug 13 2006

Extensions

Meaningful name from Joerg Arndt, Dec 26 2022

Edited by G. C. Greubel, Jul 20 2023

Status

approved