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A163415
a(n) = 18*a(n-1) - 79*a(n-2) for n>1, a(0)=1, a(1)=13.
3
1, 13, 155, 1763, 19489, 211525, 2267819, 24110267, 254827105, 2682176797, 28147841051, 294769171955, 3082165652161, 32192217154453, 335968822259435, 3504253645468043, 36535028659929409, 380794477886753965
OFFSET
0,2
COMMENTS
Binomial transform of A163414. Inverse binomial transform of A163416.
FORMULA
a(n) = ((1+2*sqrt(2))*(9+sqrt(2))^n + (1-2*sqrt(2))*(9-sqrt(2))^n)/2.
G.f.: (1-5*x)/(1-18*x+79*x^2).
E.g.f.: exp(9*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 21 2016
MATHEMATICA
LinearRecurrence[{18, -79}, {1, 13}, 50] (* G. C. Greubel, Dec 21 2016 *)
PROG
(Magma) [n le 2 select 12*n-11 else 18*Self(n-1)-79*Self(n-2): n in [1..18]];
(PARI) Vec((1-5*x)/(1-18*x+79*x^2) + O(x^50)) \\ G. C. Greubel, Dec 21 2016
CROSSREFS
Sequence in context: A252972 A108366 A204766 * A077416 A192092 A297454
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Jul 27 2009
STATUS
approved