A163308 a(n) = 16*a(n-1) - 59*a(n-2) for n > 1; a(0) = 1, a(1) = 9.

1, 9, 85, 829, 8249, 83073, 842477, 8578325, 87547057, 894631737, 9148831429, 93598030381, 957787431785, 9802315116081, 100327583381981, 1026904742262917, 10511148456669793, 107590995513204585

Offset: 0

Author

Klaus Brockhaus, Jul 24 2009

Keywords

• nonn

Comments

Binomial transform of A163307. Inverse binomial transform of A163309.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..985
• Index entries for linear recurrences with constant coefficients, signature (16, -59).

Crossrefs

Cf. A163307, A163309.

Programs

Magma

[ n le 2 select 8*n-7 else 16*Self(n-1)-59*Self(n-2): n in [1..18] ];

Mathematica

LinearRecurrence[{16,-59},{1,9},20] (* Harvey P. Dale, Dec 06 2013 *)

PARI

Vec((1-7*x)/(1-16*x+59*x^2) + O(x^50)) \\ G. C. Greubel, Dec 18 2016

Formula

a(n) = ((5+sqrt(5))*(8+sqrt(5))^n + (5-sqrt(5))*(8-sqrt(5))^n)/10.

G.f.: (1-7*x)/(1-16*x+59*x^2).

E.g.f.: (1/5)*exp(8*x)*(5*cosh(sqrt(5)*x) + sqrt(5)*sinh(sqrt(5)*x)). - G. C. Greubel, Dec 18 2016