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A162816
a(n) = 12*a(n-1)-33*a(n-2) for n > 1; a(0) = 5, a(1) = 33.
0
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.
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
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Jul 14 2009
STATUS
approved