OFFSET
1,1
COMMENTS
Also values of x (or y) in the solutions to x^2 - 3xy + y^2 + 55 = 0.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Project Euler, Problem 140: Modified Fibonacci golden nuggets
Index entries for linear recurrences with constant coefficients, signature (0,3,0,-1).
FORMULA
G.f.: -x*(x-1)*(7*x^2+15*x+7) / ((x^2-x-1)*(x^2+x-1)).
a(n) = 3*a(n-2)-a(n-4).
MATHEMATICA
CoefficientList[Series[-(x - 1) (7 x^2 + 15 x + 7) / ((x^2 - x - 1) (x^2 + x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 17 2013 *)
LinearRecurrence[{0, 3, 0, -1}, {7, 8, 13, 17}, 40] (* Harvey P. Dale, Jun 01 2020 *)
PROG
(PARI) Vec(-x*(x-1)*(7*x^2+15*x+7)/((x^2-x-1)*(x^2+x-1)) + O(x^100))
(Magma) I:=[7, 8, 13, 17]; [n le 4 select I[n] else 3*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Aug 17 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Aug 16 2013
STATUS
approved