A163476 a(n) = 20*a(n-1) - 97*a(n-2) for n > 1; a(0) = 3, a(1) = 33.

3, 33, 369, 4179, 47787, 550377, 6372201, 74057451, 863045523, 10077337713, 117831338529, 1379125012419, 16152860411067, 189282082016697, 2218814180460441, 26015921653589211, 305093457567121443

Offset: 0

Author

Klaus Brockhaus, Aug 11 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A163475. Tenth binomial transform of A056449.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..930
• Index entries for linear recurrences with constant coefficients, signature (20,-97).

Crossrefs

Cf. A163475, A056449.

Programs

Magma

[ n le 2 select 30*n-27 else 20*Self(n-1)-97*Self(n-2): n in [1..17] ];

Mathematica

LinearRecurrence[{20, -97}, {3, 33}, 50] (* G. C. Greubel, Jul 26 2017 *)

PARI

x='x+O('x^50); Vec((3-27*x)/(1-20*x+97*x^2)) \\ G. C. Greubel, Jul 26 2017

Formula

a(n) = ((3+sqrt(3))*(10+sqrt(3))^n + (3-sqrt(3))*(10-sqrt(3))^n)/2.

G.f.: (3-27*x)/(1-20*x+97*x^2).

E.g.f.: exp(10*x)*( 3*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x) ). - G. C. Greubel, Jul 26 2017