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 (12,-33).
FORMULA
a(n) = ((3+sqrt(3))*(6+sqrt(3))^n + (3-sqrt(3))*(6-sqrt(3))^n)/2.
G.f.: (3-15*x)/(1-12*x+33*x^2).
E.g.f.: exp(6*x)*( 3*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x) ). - G. C. Greubel, Jul 26 2017
MATHEMATICA
LinearRecurrence[{12, -33}, {3, 21}, 50] (* G. C. Greubel, Jul 26 2017 *)
PROG
(Magma) [ n le 2 select 18*n-15 else 12*Self(n-1)-33*Self(n-2): n in [1..20] ];
(PARI) x='x+O('x^50); Vec((3-15*x)/(1-12*x+33*x^2)) \\ G. C. Greubel, Jul 26 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Aug 11 2009
STATUS
approved