A162815 a(n) = 8*a(n-1)-13*a(n-2) for n > 1; a(0) = 5, a(1) = 23.

5, 23, 119, 653, 3677, 20927, 119615, 684869, 3923957, 22488359, 128895431, 738814781, 4234877645, 24274429007, 139142022671, 797568604277, 4571702539493, 26205228460343, 150209694669335, 861009587370221

Offset: 0

Author

Klaus Brockhaus, Jul 18 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A162814. Inverse binomial transform of A143647.

Links

• Index entries for linear recurrences with constant coefficients, signature (8,-13)

Crossrefs

Cf. A162814, A143647.

Programs

Magma

[ n le 2 select 18*n-13 else 8*Self(n-1)-13*Self(n-2): n in [1..20] ];

Mathematica

LinearRecurrence[{8,-13},{5,23},20] (* Harvey P. Dale, Aug 25 2017 *)

Formula

a(n) = ((5+sqrt(3))*(4+sqrt(3))^n+(5-sqrt(3))*(4-sqrt(3))^n)/2.

G.f.: (5-17*x)/(1-8*x+13*x^2).