OFFSET
1,2
COMMENTS
Also y-values in the solution of x^2-5*y^2=44.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,3,0,-1).
FORMULA
G.f.: x*(x+1)*(x^2+x+1) / ((x^2-x-1)*(x^2+x-1)).
a(n) = 3*a(n-2)-a(n-4).
Let h(n) = hypergeom([(1 - n)/2, (n + 1) mod 2 - n/2], [1 - n], -4) then a(n) = h(n-1) + h(n) for n > 2. - Peter Luschny, Sep 03 2019
MATHEMATICA
CoefficientList[Series[(x + 1) (x^2 + x + 1) / ((x^2 - x - 1) (x^2 + x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 17 2013 *)
PROG
(PARI) Vec(x*(x+1)*(x^2+x+1)/((x^2-x-1)*(x^2+x-1)) + O(x^100))
(Magma) I:=[1, 2, 5, 7, 14]; [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