OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..975
Index entries for linear recurrences with constant coefficients, signature (18,-79).
FORMULA
a(n) = ((1+sqrt(2))*(9+sqrt(2))^n + (1-sqrt(2))*(9-sqrt(2))^n)/2.
G.f.: (1-7*x)/(1-18*x+79*x^2).
E.g.f.: exp(9*x)*( cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 23 2016
MATHEMATICA
LinearRecurrence[{18, -79}, {1, 11}, 50] (* G. C. Greubel, Dec 23 2016 *)
PROG
(Magma) [ n le 2 select 10*n-9 else 18*Self(n-1)-79*Self(n-2): n in [1..18] ];
(PARI) Vec((1-7*x)/(1-18*x+79*x^2) + O(x^50)) \\ G. C. Greubel, Dec 23 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Jul 27 2009
STATUS
approved