A163148 - OEIS

%I #7 Sep 08 2022 08:45:46

%S 1,13,149,1617,17081,177893,1838509,18920457,194255281,1991777533,

%T 20407378949,209003188737,2140015661801,21909062453333,

%U 224284075207069,2295910518566457,23501807859846241,240570205162118893

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

%C Binomial transform of A163147.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,-59).

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

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

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

%o (PARI) Vec((1-3*x)/(1-16*x+59*x^2) + O(x^30)) \\ _Jinyuan Wang_, Mar 23 2020

%Y Cf. A163147.

%K nonn

%O 0,2

%A _Klaus Brockhaus_, Jul 21 2009