OFFSET
0,1
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-16,7,23,-28,-3,17,-4,-3,1).
FORMULA
G.f.: -(4*x^9-8*x^8+36*x^7-115*x^6+86*x^5+70*x^4-162*x^3+130*x^2-54*x+9) / ((x-1)^3*(x+1)*(x^2-3*x+1)*(x^2+x-1)^2). - Colin Barker, Apr 24 2015
MATHEMATICA
Table[(Fibonacci[n+1]+LucasL[n]+n)^2, {n, 0, 50}] (* or *) LinearRecurrence[ {7, -16, 7, 23, -28, -3, 17, -4, -3, 1}, {9, 9, 49, 100, 256, 576, 1369, 3249, 7921, 19600}, 50] (* Harvey P. Dale, Oct 04 2017 *)
PROG
(PARI) lucas(n) = if(n==0, 2, fibonacci(2*n)/fibonacci(n))
a(n) = (fibonacci(n+1)+lucas(n)+n)^2 \\ Colin Barker, Apr 24 2015
(PARI) Vec(-(4*x^9-8*x^8+36*x^7-115*x^6+86*x^5+70*x^4-162*x^3+130*x^2-54*x+9) / ((x-1)^3*(x+1)*(x^2-3*x+1)*(x^2+x-1)^2) + O(x^100)) \\ Colin Barker, Apr 24 2015
(PARI) a(n)=(fibonacci(n-1)+2*fibonacci(n+1)+n)^2 \\ Charles R Greathouse IV, Apr 24 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Name corrected by Colin Barker, Apr 24 2015
STATUS
approved