A163309 a(n) = 18*a(n-1) - 76*a(n-2) for n > 1; a(0) = 1, a(1) = 10.

1, 10, 104, 1112, 12112, 133504, 1482560, 16539776, 185041408, 2073722368, 23263855616, 261146501120, 2932583993344, 32939377795072, 370032416817152, 4157190790283264, 46706970546995200, 524778969784385536

Offset: 0

Author

Klaus Brockhaus, Jul 24 2009

Keywords

• nonn

Comments

Binomial transform of A163308. Inverse binomial transform of A163310.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..950
• Index entries for linear recurrences with constant coefficients, signature (18,-76).

Crossrefs

Cf. A163308, A163310.

Programs

Magma

[ n le 2 select 9*n-8 else 18*Self(n-1)-76*Self(n-2): n in [1..18] ];

Mathematica

LinearRecurrence[{18,-76}, {1,10}, 50] (* G. C. Greubel, Dec 18 2016 *)

PARI

Vec((1-8*x)/(1-18*x+76*x^2) + O(x^50)) \\ G. C. Greubel, Dec 18 2016

Formula

a(n) = ((5+sqrt(5))*(9+sqrt(5))^n + (5-sqrt(5))*(9-sqrt(5))^n)/10.

G.f.: (1-8*x)/(1-18*x+76*x^2).

E.g.f.: (1/5)*exp(9*x)*(5*cosh(sqrt(5)*x) + sqrt(5)*sinh(sqrt(5)*x)). - G. C. Greubel, Dec 18 2016