OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
J. V. Leyendekkers and A. G. Shannon, Pellian sequence relationships among pi, e, sqrt(2), Notes on Number Theory and Discrete Mathematics, Vol. 18, 2012, No. 2, 58-62. See Table 3, {y_n}.
Index entries for linear recurrences with constant coefficients, signature (6,0,-6,1).
FORMULA
From Bruno Berselli, Dec 26 2012: (Start)
G.f.: x*(1+11*x-5*x^2+x^3)/((1-x)*(1+x)*(1-6*x+x^2)).
a(n) = a(-n) = 6*a(n-1)-6*a(n-3)+a(n-4).
a(n) = ((1+sqrt(2))^(2n)+(1-sqrt(2))^(2n))/2+(-1)^n-1.
a(n) = 2*A090390(n)-1. (End)
MATHEMATICA
CoefficientList[Series[(1 + 11 x - 5 x^2 + x^3)/((1 - x) (1 + x) (1 - 6 x + x^2)), {x, 0, 24}], x] (* Bruno Berselli, Dec 26 2012 *)
PROG
(Magma) /* By definition: */ a:=[1, 17]; c:=func<n | IsOdd(n) select -4 else 12>; [n le 2 select a[n] else 6*Self(n-1)-Self(n-2)+c(n): n in [1..22]]; // Bruno Berselli, Dec 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 23 2012
EXTENSIONS
Edited from Bruno Berselli, Dec 26 2012
STATUS
approved