A163444 a(n) = 12*a(n-1) - 34*a(n-2) for n > 1; a(0) = 1, a(1) = 8.

1, 8, 62, 472, 3556, 26624, 198584, 1477792, 10981648, 81534848, 605042144, 4488320896, 33288417856, 246858103808, 1830491038592, 13572716933632, 100635907891456, 746158518953984, 5532281359138304, 41017986665224192

Offset: 0

Author

Klaus Brockhaus, Jul 27 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A163346. Inverse binomial transform of A163445.

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. A163346, A163445.

Programs

Magma

[ n le 2 select 7*n-6 else 12*Self(n-1)-34*Self(n-2): n in [1..20] ];

Mathematica

LinearRecurrence[{12,-34}, {1,8}, 50] (* G. C. Greubel, Dec 23 2016 *)

PARI

Vec((1-4*x)/(1-12*x+34*x^2) + O(x^50)) \\ G. C. Greubel, Dec 23 2016

Formula

a(n) = ((1+sqrt(2))*(6+sqrt(2))^n + (1-sqrt(2))*(6-sqrt(2))^n)/2.

G.f.: (1-4*x)/(1-12*x+34*x^2).

E.g.f.: 2*exp(6*x)*( cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 23 2016