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 *)
Rest[CoefficientList[Series[2x^2(305-727x-315x^2+60x^3)/((1-x)(1-7x+x^2)(1+3x+x^2)), {x, 0, 30}], x]] (* Harvey P. Dale, Oct 17 2024 *)
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
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