A214982 a(n) = (Fibonacci(5n)/Fibonacci(n) - 5)/50.

0, 1, 6, 45, 300, 2080, 14196, 97461, 667590, 4576825, 31367160, 215001216, 1473620616, 10100397385, 69229018950, 474503107365, 3252291758436, 22291541752096, 152788493829180, 1047227932532925, 7177806988136070

Offset: 1

Author

Clark Kimberling, Oct 28 2012

Keywords

• nonn

Comments

See the comments at A028412.

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (5, 15, -15, -5, 1).

Crossrefs

Cf. A000045, A028412.

Programs

Mathematica

(See A028412.)
Table[(Fibonacci[5n]/Fibonacci[n]-5)/50,{n,25}] (* or *) LinearRecurrence[ {5,15,-15,-5,1},{0,1,6,45,300},30] (* Harvey P. Dale, Nov 03 2013 *)

Formula

a(n) = (Fibonacci(5n)/Fibonacci(n) - 5)/50.

Empirical G.f.: -x^2*(x+1)/((x-1)*(x^2-7*x+1)*(x^2+3*x+1)). - Colin Barker, Nov 22 2012

a(n) = 5*a(n-1) + 15*a(n-2) - 15*a(n-3) - 5*a(n-4) + a(n-5), with a(1)=0, a(2)=1, a(3)=6, a(4)=45, a(5)=300. - Harvey P. Dale, Nov 03 2013

a(n) = (1/2)*Fibonacci(n)^2*(Fibonacci(n)^2 + (-1)^n) shows that a(n) is always an integer. - Peter Bala, Nov 29 2013