OFFSET
0,2
COMMENTS
For the general computation of the o.g.f.s for the trisection of a sequence, given by its real o.g.f., see a Wolfdieter Lang comment under A187357.
LINKS
Colin Barker, Table of n, a(n) for n = 0..850
Index entries for linear recurrences with constant coefficients, signature (14,1).
FORMULA
a(n) = Pell(3*n+1), n >= 0, with Pell(n):=A000129(n).
O.g.f.: (1-2*x)/(1-14*x-x^2).
a(n) = 14*a(n-1) + a(n-2), a(0)= 1, a(1)=12.
a(n) = (((7-5*sqrt(2))^n*(-1+sqrt(2))+(1+sqrt(2))*(7+5*sqrt(2))^n))/(2*sqrt(2)). - Colin Barker, Jan 25 2016
MATHEMATICA
Table[Fibonacci[3n + 1, 2], {n, 0, 20}] (* Vladimir Reshetnikov, Sep 16 2016 *)
LinearRecurrence[{14, 1}, {1, 12}, 20] (* Harvey P. Dale, Jul 06 2023 *)
PROG
(PARI) Vec((1-2*x)/(1-14*x-x^2) + O(x^20)) \\ Colin Barker, Jan 25 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Mar 09 2011
STATUS
approved