A163310 a(n) = 20*a(n-1) - 95*a(n-2) for n > 1; a(0) = 1, a(1) = 11.

1, 11, 125, 1455, 17225, 206275, 2489125, 30186375, 367260625, 4477506875, 54660378125, 667844409375, 8164152265625, 99837826421875, 1221162063203125, 14938647753984375, 182762559075390625, 2236079644879296875

Offset: 0

Author

Klaus Brockhaus, Jul 24 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A163309. Tenth binomial transform of A074872.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..915
• Index entries for linear recurrences with constant coefficients, signature (20,-95).

Crossrefs

Cf. A163309, A074872.

Programs

Magma

[ n le 2 select 10*n-9 else 20*Self(n-1)-95*Self(n-2): n in [1..18] ];

Mathematica

LinearRecurrence[{20,-95}, {1,11}, 50] (* G. C. Greubel, Dec 18 2016 *)

PARI

Vec((1-9*x)/(1-20*x+95*x^2) + O(x^50)) \\ G. C. Greubel, Dec 18 2016

Formula

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

G.f.: (1-9*x)/(1-20*x+95*x^2).

E.g.f.: (1/5)*exp(10*x)*(5*cosh(sqrt(5)*x) + sqrt(5)*sinh(sqrt(5)*x)). - G. C. Greubel, Dec 18 2016