A163475 a(n) = 18*a(n-1) - 78*a(n-2) for n > 1; a(0) = 3, a(1) = 30.

3, 30, 306, 3168, 33156, 349704, 3708504, 39476160, 421307568, 4504395744, 48217133088, 516565527552, 5537243115072, 59378264922240, 636903805624704, 6832763837309952, 73311252232852224, 786646960881163776

Offset: 0

Author

Klaus Brockhaus, Aug 11 2009

Keywords

• nonn

Comments

Binomial transform of A163474. Inverse binomial transform of A163476.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..965
• Index entries for linear recurrences with constant coefficients, signature (18,-78).

Crossrefs

Cf. A163474, A163476.

Programs

Magma

[ n le 2 select 27*n-24 else 18*Self(n-1)-78*Self(n-2): n in [1..18] ];

Mathematica

LinearRecurrence[{18, -78}, {3, 30}, 50] (* G. C. Greubel, Jul 26 2017 *)

PARI

x='x+O('x^50); Vec((3-24*x)/(1-18*x+78*x^2)) \\ G. C. Greubel, Jul 26 2017

Formula

a(n) = ((3+sqrt(3))*(9+sqrt(3))^n + (3-sqrt(3))*(9-sqrt(3))^n)/2.

G.f.: (3-24*x)/(1-18*x+78*x^2).

E.g.f.: exp(9*x)*( 3*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x) ). - G. C. Greubel, Jul 26 2017