OFFSET
1,3
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).
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
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Oct 28 2012
STATUS
approved