A165311 - OEIS

%I #9 Jul 14 2015 09:44:04

%S 1,4,20,116,724,4660,30356,198644,1302100,8540596,56031764,367636340,

%T 2412218836,15827788084,103854591380,681446713076,4471346955604,

%U 29338975191220,192509225431316,1263159425822324,8288287225499860

%N a(0)=1, a(1)=4, a(n)=9*a(n-1)-16*a(n-2) for n>1.

%C a(n)/a(n-1) tends to (9+sqrt(17))/2 = 6.56155281...

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-16).

%F G.f.: (1-5x)/(1-9x+16x^2). a(n)=Sum_{k, 0<=k<=n}A165253(n,k)*4^(n-k).

%F a(n) = ((17-sqrt(17))*(9+sqrt(17))^n+(17+sqrt(17))*(9-sqrt(17))^n )/(34*2^n). [From _Klaus Brockhaus_, Sep 26 2009]

%t LinearRecurrence[{9,-16},{1,4},30] (* _Harvey P. Dale_, Feb 19 2015 *)

%K nonn

%O 0,2

%A _Philippe Deléham_, Sep 14 2009