OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-13).
FORMULA
a(n) = ((3+sqrt(3))*(4+sqrt(3))^n + (3-sqrt(3))*(4-sqrt(3))^n)/2.
G.f.: (3-9*x)/(1-8*x+13*x^2).
a(n) = 3*A162557(n). - R. J. Mathar, Jun 14 2016
E.g.f.: (1/2)*exp(4*x)*(6*cosh(sqrt(3)*x) + 2*sqrt(3)*sinh(sqrt(3)*x)). - G. C. Greubel, Jul 25 2017
MATHEMATICA
LinearRecurrence[{8, -13}, {3, 15}, 50] (* G. C. Greubel, Jul 25 2017 *)
PROG
(Magma) [ n le 2 select 12*n-9 else 8*Self(n-1)-13*Self(n-2): n in [1..22] ];
(PARI) x='x+O('x^50); Vec((3-9*x)/(1-8*x+13*x^2)) \\ G. C. Greubel, Jul 25 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Aug 11 2009
STATUS
approved