A164021 a(n) = 12*a(n-1) - 34*a(n-2) for n > 1; a(0) = 3, a(1) = 22.

3, 22, 162, 1196, 8844, 65464, 484872, 3592688, 26626608, 197367904, 1463110176, 10846813376, 80416014528, 596200519552, 4420261740672, 32772323223296, 242978979496704, 1801488764368384, 13356579869532672, 99028340445867008

Offset: 0

Author

Klaus Brockhaus, Aug 08 2009

Keywords

• nonn

Comments

Binomial transform of A163605.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (12, -34).

Crossrefs

Cf. A163605.

Programs

Magma

[ n le 2 select 19*n-16 else 12*Self(n-1)-34*Self(n-2): n in [1..20] ];

Mathematica

LinearRecurrence[{12,-34},{3,22},20] (* Harvey P. Dale, Oct 19 2012 *)

PARI

x='x+O('x^50); Vec((3-14*x)/(1-12*x+34*x^2)) \\ G. C. Greubel, Sep 07 2017

Formula

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

G.f.: (3-14*x)/(1-12*x+34*x^2).

E.g.f.: (3*cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x))*exp(6*x). - G. C. Greubel, Sep 07 2017