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

0,2

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).

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

Mathematica

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

Prog

(Magma) [ n le 2 select 10*n-9 else 20*Self(n-1)-95*Self(n-2): n in [1..18] ];
(PARI) Vec((1-9*x)/(1-20*x+95*x^2) + O(x^50)) \\ G. C. Greubel, Dec 18 2016

Crossrefs

Cf. A163309, A074872.

Sequence in context: A282755 A242523 A015596 * A240335 A076483 A209901

Adjacent sequences: A163307 A163308 A163309 * A163311 A163312 A163313

Keyword

nonn,easy

Author

Klaus Brockhaus, Jul 24 2009

Status

approved