A163471 a(n) = 10*a(n-1) - 22*a(n-2) for n > 1; a(0) = 3, a(1) = 18.

3, 18, 114, 744, 4932, 32952, 221016, 1485216, 9989808, 67223328, 452457504, 3045661824, 20502553152, 138020971392, 929153544576, 6255074075136, 42109362770688, 283481998053888, 1908413999583744, 12847536038651904

Offset

0,1

Comments

Binomial transform of A163470. Inverse binomial transform of A163472.

Links

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

Index entries for linear recurrences with constant coefficients, signature (10,-22).

Formula

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

G.f.: (3-12*x)/(1-10*x+22*x^2).

E.g.f.: exp(5*x)*( 3*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x) ). - G. C. Greubel, Jul 26 2017

Mathematica

LinearRecurrence[{10, -22}, {3, 18}, 50] (* G. C. Greubel, Jul 26 2017 *)

Prog

(Magma) [ n le 2 select 15*n-12 else 10*Self(n-1)-22*Self(n-2): n in [1..20] ];
(PARI) x='x+O('x^50); Vec((3-12*x)/(1-10*x+22*x^2)) \\ G. C. Greubel, Jul 26 2017

Crossrefs

Cf. A163470, A163472.

Sequence in context: A346578 A213099 A199259 * A054122 A213230 A201695

Adjacent sequences: A163468 A163469 A163470 * A163472 A163473 A163474

Keyword

nonn

Author

Klaus Brockhaus, Aug 11 2009

Status

approved