OFFSET
0,2
COMMENTS
Values of Y are given by c(n)*(d(n)-1) and listed in A123115.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (40,-206,40,-1).
FORMULA
a(n) = c(n)*(d(n) + 1), where c(0) = 0, c(1) = 1, c(n) = 6*c(n-1) - c(n-2) and d(0) = 1, d(1) = 3, d(n) = 6*d(n-1) - d(n-2).
For n >= 4, a(n) = 40*a(n-1) - 206*a(n-2) + 40*a(n-3) - a(n-4). - Max Alekseyev, Nov 12 2009
G.f.: 4*x*(1 -13*x +x^2)/((1-34*x+x^2)*(1-6*x+x^2)). - Colin Barker, Oct 24 2012
a(n) = (1/4)*(A000129(4*n) + 2*A000129(2*n)) = (1/4)*A000129(2*n)*(A002203(2*n) + 2). - G. C. Greubel, Jul 20 2021
MATHEMATICA
Table[(Fibonacci[4*n, 2] + 2*Fibonacci[2*n, 2])/4, {n, 0, 30}] (* G. C. Greubel, Jul 20 2021 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); [0] cat Coefficients(R!( 4*x*(1 -13*x +x^2)/((1-34*x+x^2)*(1-6*x+x^2)) )); // G. C. Greubel, Jul 20 2021
(Sage) [(1/4)*(lucas_number1(4*n, 2, -1) + 2*lucas_number1(2*n, 2, -1)) for n in (0..30)] # G. C. Greubel, Jul 20 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mohamed Bouhamida, Sep 26 2006
EXTENSIONS
More terms from Max Alekseyev, Nov 12 2009
STATUS
approved