login
a(0)=1, a(1)=4, a(n)=8a(n-1)-13a(n-2), n>=2.
4

%I #14 Aug 25 2016 19:21:41

%S 1,4,19,100,553,3124,17803,101812,583057,3340900,19147459,109747972,

%T 629066809,3605810836,20668618171,118473404500,679095199777,

%U 3892607339716,22312621120627,127897073548708,733112513821513

%N a(0)=1, a(1)=4, a(n)=8a(n-1)-13a(n-2), n>=2.

%C Binomial transform of A083881.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-13).

%F a(n) = ((4-sqrt(3))^n+(4+sqrt(3))^n)/2.

%F a(n) = Sum_{k=0..floor(n/2)} C(n, 2k)4^(n-2k)3^k.

%F G.f.: (1-4x)/(1-8x+13x^2);

%F E.g.f.: exp(4x)cosh(x*sqrt(3)).

%F a(n) = Sum_{k=0..n} A027907(n,2k)*3^k . - _J. Conrad_, Aug 24 2016

%t LinearRecurrence[{8,-13},{1,4},30] (* _Harvey P. Dale_, Aug 02 2015 *)

%K easy,nonn

%O 0,2

%A _Paul Barry_, May 08 2003