A163192 - OEIS

%I #8 Sep 08 2022 08:45:46

%S 1,10,107,1210,14249,172450,2123843,26439010,331262801,4166428090,

%T 52521121307,662944613770,8374427993849,105834710796370,

%U 1337872412499443,16914820145926450,213874268556080801

%N a(n) = 20*a(n-1)-93*a(n-2) for n > 1; a(0) = 1, a(1) = 10.

%C Binomial transform of A152266. Tenth binomial transform of powers of 7 interleaved with zeros.

%H Harvey P. Dale, <a href="/A163192/b163192.txt">Table of n, a(n) for n = 0..900</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20, -93).

%F a(n) = ((10+sqrt(7))^n+(10-sqrt(7))^n)/2.

%F G.f.: (1-10*x)/(1-20*x+93*x^2).

%t LinearRecurrence[{20,-93},{1,10},40] (* _Harvey P. Dale_, Nov 01 2011 *)

%o (Magma) [ n le 2 select 9*n-8 else 20*Self(n-1)-93*Self(n-2): n in [1..17] ];

%Y Cf. A152266, A000420 (powers of 7).

%K nonn

%O 0,2

%A _Klaus Brockhaus_, Jul 22 2009