OFFSET
0,2
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (6,-4).
FORMULA
E.g.f.: exp(3*x)*cosh(sqrt(5)*x).
a(n) = ((3-sqrt(5))^n + (3+sqrt(5))^n)/2.
a(n) = 2*(3*a(n-1) - 2*a(n-2)). - Lekraj Beedassy, Oct 22 2004
a(n) = 2^(n-1)*Lucas(2*n). - Eric W. Weisstein, Mar 31 2017
MATHEMATICA
a[n_]:=(MatrixPower[{{5, 1}, {1, 1}}, n].{{2}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2010 *)
CoefficientList[Series[(1-3x)/(1-6x+4x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{6, -4}, {1, 3}, 31] (* Harvey P. Dale, Jun 06 2011 *)
Table[2^(n - 1) LucasL[2 n], {n, 0, 20}] (* Eric W. Weisstein, Mar 31 2017 *)
PROG
(PARI) Vec((1-3*x)/(1 - 6*x + 4*x^2) + O(x^25)) \\ Jinyuan Wang, Jul 24 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Sep 18 2004
STATUS
approved