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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Binomial transform of A163471. Inverse binomial transform of A163473.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

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

Cf. A163471, A163473.

Sequence in context: A007566 A183412 A155627 * A229809 A074575 A091171

Adjacent sequences:  A163469 A163470 A163471 * A163473 A163474 A163475

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Aug 11 2009

STATUS

approved

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Last modified March 18 12:10 EDT 2019. Contains 321283 sequences. (Running on oeis4.)