A162814 a(n) = 6*a(n-1)-6*a(n-2) for n > 1; a(0) = 5, a(1) = 18.

5, 18, 78, 360, 1692, 7992, 37800, 178848, 846288, 4004640, 18950112, 89672832, 424336320, 2007980928, 9501867648, 44963320320, 212768716032, 1006832374272, 4764381949440, 22545297451008, 106685493009408, 504841173350400

Offset

0,1

Comments

Binomial transform of A162563. Inverse binomial transform of A162815.

Links

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (6,-6).

Formula

a(n) = ((5+sqrt(3))*(3+sqrt(3))^n+(5-sqrt(3))*(3-sqrt(3))^n)/2.

G.f.: (5-12*x)/(1-6*x+6*x^2).

Mathematica

LinearRecurrence[{6, -6}, {5, 18}, 40] (* Harvey P. Dale, Mar 26 2022 *)

Prog

(Magma) [ n le 2 select 13*n-8 else 6*Self(n-1)-6*Self(n-2): n in [1..22] ];

Crossrefs

Cf. A162563, A162815.

Sequence in context: A027134 A227451 A017960 * A082034 A259340 A241713

Adjacent sequences: A162811 A162812 A162813 * A162815 A162816 A162817

Keyword

nonn

Author

Al Hakanson (hawkuu(AT)gmail.com) and Klaus Brockhaus, Jul 14 2009

Status

approved