OFFSET
1,1
COMMENTS
LINKS
Colin Barker, Table of n, a(n) for n = 1..797
Index entries for linear recurrences with constant coefficients, signature (17,17,-1).
FORMULA
From Colin Barker, Jun 04 2015: (Start)
a(n) = 17*a(n-1) + 17*a(n-2) - a(n-3).
G.f.: x*(15 + 18*x - x^2)/((1+x)*(1-18*x+x^2)). - Colin Barker, Jun 04 2015
a(n) = ((-1)^n + (2+sqrt(5))*(9+4*sqrt(5))^n + (2-sqrt(5))*(9+4*sqrt(5))^(-n))/5. - Colin Barker, Mar 04 2016
From G. C. Greubel, Feb 13 2023: (Start)
a(n) = Fibonacci(3*n+1)*Fibonacci(3*n+2).
a(n) = (1/5)*(4*A049629(n) + (-1)^n - 5*[n=0]). (End)
MATHEMATICA
LinearRecurrence[{17, 17, -1}, {15, 273, 4895}, 40] (* G. C. Greubel, Feb 13 2023 *)
PROG
(PARI) Vec(x*(15+18*x-x^2)/((1+x)*(1-18*x+x^2)) + O(x^50)) \\ Colin Barker, Jun 04 2015
(Magma) [Fibonacci(3*n+1)*Fibonacci(3*n+2): n in [1..40]]; // G. C. Greubel, Feb 13 2023
(SageMath) [fibonacci(3*n+1)*fibonacci(3*n+2) for n in range(1, 41)] # G. C. Greubel, Feb 13 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Sep 22 2011
STATUS
approved