A163445 a(n) = 14*a(n-1) - 47*a(n-2) for n > 1; a(0) = 1, a(1) = 9.

1, 9, 79, 683, 5849, 49785, 422087, 3569323, 30132433, 254095881, 2141117983, 18033145355, 151831489769, 1278083025081, 10757082331991, 90529250469067, 761826636963361, 6410698145440905, 53943922098894703, 453912096548803307

Offset

0,2

Comments

Binomial transform of A163444. Inverse binomial transform of A163446.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (14,-47).

Formula

a(n) = ((1+sqrt(2))*(7+sqrt(2))^n + (1-sqrt(2))*(7-sqrt(2))^n)/2.

G.f.: (1-5*x)/(1-14*x+47*x^2).

E.g.f.: exp(7*x)*( cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 23 2016

Mathematica

LinearRecurrence[{14, -47}, {1, 9}, 50] (* G. C. Greubel, Dec 23 2016 *)

Prog

(Magma) [ n le 2 select 8*n-7 else 14*Self(n-1)-47*Self(n-2): n in [1..20] ];
(PARI) Vec((1-5*x)/(1-14*x+47*x^2) + O(x^50)) \\ G. C. Greubel, Dec 23 2016

Crossrefs

Cf. A163444, A163446.

Sequence in context: A294344 A125909 A125421 * A190979 A254598 A083411

Adjacent sequences: A163442 A163443 A163444 * A163446 A163447 A163448

Keyword

nonn

Author

Klaus Brockhaus, Jul 27 2009

Status

approved