A164110 a(n) = 12*a(n-1) - 34*a(n-2) for n > 1; a(0) = 5, a(1) = 36.

5, 36, 262, 1920, 14132, 104304, 771160, 5707584, 42271568, 313200960, 2321178208, 17205305856, 127543611200, 945542935296, 7010032442752, 51971929512960, 385322051101952, 2856819009782784, 21180878379927040

Offset: 0

Author

Klaus Brockhaus, Aug 10 2009

Keywords

• nonn

Comments

Binomial transform of A164038. Sixth binomial transform of A164095.

Links

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

Crossrefs

Cf. A164038, A164095.

Programs

Magma

[ n le 2 select 31*n-26 else 12*Self(n-1)-34*Self(n-2): n in [1..19] ];

Mathematica

LinearRecurrence[{12,-34}, {5,36}, 50] (* G. C. Greubel, Sep 11 2017 *)

PARI

x='x+O('x^50); Vec((5-24*x)/(1-12*x+34*x^2)) \\ G. C. Greubel, Sep 11 2017

Formula

a(n) = ((5+3*sqrt(2))*(6+sqrt(2))^n+(5-3*sqrt(2))*(6-sqrt(2))^n)/2.

G.f.: (5-24*x)/(1-12*x+34*x^2).

E.g.f.: (5*cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x))*exp(6*x). - G. C. Greubel, Sep 11 2017