A163458 a(n) = 12*a(n-1) - 34*a(n-2) for n > 1; a(0) = 1, a(1) = 7.

1, 7, 50, 362, 2644, 19420, 143144, 1057448, 7822480, 57916528, 429034016, 3179246240, 23563798336, 174671207872, 1294885351040, 9599803144832, 71171535802624, 527665122707200, 3912149255197184, 29005176890321408

Offset: 0

Author

Klaus Brockhaus, Jul 28 2009

Keywords

• nonn

Comments

Binomial transform of A161734. Inverse binomial transform of A163459.

Links

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

Crossrefs

Cf. A161734, A163459.

Programs

Magma

[ n le 2 select 6*n-5 else 12*Self(n-1)-34*Self(n-2): n in [1..20] ];

Mathematica

LinearRecurrence[{12,-34},{1,7},40] (* Harvey P. Dale, Aug 25 2015 *)

PARI

Vec((1-5*x)/(1-12*x+34*x^2) + O(x^50)) \\ G. C. Greubel, Dec 24 2016

Formula

a(n) = ((2+sqrt(2))*(6+sqrt(2))^n + (2-sqrt(2))*(6-sqrt(2))^n)/4.

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

E.g.f.: (1/2)*exp(6*x)*(sqrt(2)*sinh(sqrt(2)*x) + 2*cosh(sqrt(2)*x)). - G. C. Greubel, Dec 24 2016