OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..965
Index entries for linear recurrences with constant coefficients, signature (18,-78).
FORMULA
a(n) = ((3+sqrt(3))*(9+sqrt(3))^n + (3-sqrt(3))*(9-sqrt(3))^n)/2.
G.f.: (3-24*x)/(1-18*x+78*x^2).
E.g.f.: exp(9*x)*( 3*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x) ). - G. C. Greubel, Jul 26 2017
MATHEMATICA
LinearRecurrence[{18, -78}, {3, 30}, 50] (* G. C. Greubel, Jul 26 2017 *)
PROG
(Magma) [ n le 2 select 27*n-24 else 18*Self(n-1)-78*Self(n-2): n in [1..18] ];
(PARI) x='x+O('x^50); Vec((3-24*x)/(1-18*x+78*x^2)) \\ G. C. Greubel, Jul 26 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Aug 11 2009
STATUS
approved