A162816 a(n) = 12*a(n-1)-33*a(n-2) for n > 1; a(0) = 5, a(1) = 33.

5, 33, 231, 1683, 12573, 95337, 729135, 5603499, 43180533, 333250929, 2574053559, 19891362051, 153752577165, 1188615978297, 9189556693119, 71050353033627, 549348865530597, 4247524736257473, 32841784272579975, 253933094974463091

Offset

0,1

Comments

Binomial transform of A143647.

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (12,-33).

Formula

a(n) = ((5+sqrt(3))*(6+sqrt(3))^n+(5-sqrt(3))*(6-sqrt(3))^n)/2.

G.f.: (5-27*x)/(1-12*x+33*x^2).

Mathematica

LinearRecurrence[{12, -33}, {5, 33}, 40] (* or *) Simplify[With[ {c=Sqrt[3]}, Table[(11(5+c)(6+c)^n+(53+7c)(6-c)^n)/(22(6+c)), {n, 30}]]] (* Harvey P. Dale, Jun 30 2011 *)

Prog

(Magma) [ n le 2 select 28*n-23 else 12*Self(n-1)-33*Self(n-2): n in [1..20] ];
(PARI) Vec((5-27*x)/(1-12*x+33*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jun 30 2011

Crossrefs

Cf. A143647.

Sequence in context: A221441 A083076 A361237 * A128418 A335119 A284733

Adjacent sequences: A162813 A162814 A162815 * A162817 A162818 A162819

Keyword

nonn,easy

Author

Klaus Brockhaus, Jul 14 2009

Status

approved