A163148 a(n) = 16*a(n-1) - 59*a(n-2) for n > 1; a(0) = 1, a(1) = 13.

1, 13, 149, 1617, 17081, 177893, 1838509, 18920457, 194255281, 1991777533, 20407378949, 209003188737, 2140015661801, 21909062453333, 224284075207069, 2295910518566457, 23501807859846241, 240570205162118893

Offset: 0

Author

Klaus Brockhaus, Jul 21 2009

Keywords

• nonn

Comments

Binomial transform of A163147.

Links

• Index entries for linear recurrences with constant coefficients, signature (16,-59).

Crossrefs

Cf. A163147.

Programs

Magma

[ n le 2 select 12*n-11 else 16*Self(n-1)-59*Self(n-2): n in [1..18] ];

PARI

Vec((1-3*x)/(1-16*x+59*x^2) + O(x^30)) \\ Jinyuan Wang, Mar 23 2020

Formula

a(n) = ((1+sqrt(5))*(8+sqrt(5))^n+(1-sqrt(5))*(8-sqrt(5))^n)/2.

G.f.: (1-3*x)/(1-16*x+59*x^2).