A163474 a(n) = 16*a(n-1) - 61*a(n-2) for n > 1; a(0) = 3, a(1) = 27.

3, 27, 249, 2337, 22203, 212691, 2048673, 19804617, 191904819, 1862395467, 18092133513, 175868012721, 1710268059243, 16636340171907, 161855091136689, 1574864707700697, 15324674763873123, 149128049052227451

Offset: 0

Author

Klaus Brockhaus, Aug 11 2009

Keywords

• nonn

Comments

Binomial transform of A163473. Inverse binomial transform of A163475.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (16,-61).

Crossrefs

Cf. A163473, A163475.

Programs

Magma

[ n le 2 select 24*n-21 else 16*Self(n-1)-61*Self(n-2): n in [1..18] ];

Mathematica

LinearRecurrence[{16, -61}, {3, 27}, 50] (* G. C. Greubel, Jul 26 2017 *)

PARI

x='x+O('x^50); Vec((3-21*x)/(1-16*x+61*x^2)) \\ G. C. Greubel, Jul 26 2017

Formula

a(n) = ((3+sqrt(3))*(8+sqrt(3))^n + (3-sqrt(3))*(8-sqrt(3))^n)/2.

G.f.: (3-21*x)/(1-16*x+61*x^2).

E.g.f.: exp(8*x)*( 3*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x) ). - G. C. Greubel, Jul 26 2017