login
A163472
a(n) = 12*a(n-1) - 33*a(n-2) for n > 1; a(0) = 3, a(1) = 21.
3
3, 21, 153, 1143, 8667, 66285, 509409, 3925503, 30295539, 234004869, 1808305641, 13977507015, 108055998027, 835414244829, 6459123003057, 49940805957327, 386138612387043, 2985616752052725, 23084826815860281, 178492568972583447
OFFSET
0,1
COMMENTS
Binomial transform of A163471. Inverse binomial transform of A163473.
FORMULA
a(n) = ((3+sqrt(3))*(6+sqrt(3))^n + (3-sqrt(3))*(6-sqrt(3))^n)/2.
G.f.: (3-15*x)/(1-12*x+33*x^2).
E.g.f.: exp(6*x)*( 3*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x) ). - G. C. Greubel, Jul 26 2017
MATHEMATICA
LinearRecurrence[{12, -33}, {3, 21}, 50] (* G. C. Greubel, Jul 26 2017 *)
PROG
(Magma) [ n le 2 select 18*n-15 else 12*Self(n-1)-33*Self(n-2): n in [1..20] ];
(PARI) x='x+O('x^50); Vec((3-15*x)/(1-12*x+33*x^2)) \\ G. C. Greubel, Jul 26 2017
CROSSREFS
Sequence in context: A007566 A183412 A155627 * A229809 A074575 A091171
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Aug 11 2009
STATUS
approved