%I #5 Jun 13 2015 00:51:32
%S 1,1,4,8,24,60,168,448,1232,3344,9152,24960,68224,186304,509056,
%T 1390592,3799296,10379520,28357632,77473792,211662848,578272256,
%U 1579870208,4316282880,11792306176,32217174016,88018960384,240472260608
%N a(n)=2a(n-1)+4a(n-2)-4a(n-3)-4a(n-4).
%C Form the 6 node graph with matrix A=[1,1,1,1,0,0; 1,1,0,0,1,1; 1,0,0,0,0,0; 1,0,0,0,0,0; 0,1,0,0,0,0; 0,1,0,0,0,0]. Then A099176 counts closed walks of length n at either of the degree 5 vertices.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,-4,-4).
%F G.f.: (1+x)*(1-2*x)/((1-2x^2)(1-2x-2x^2)).
%F a(n)=(3+sqrt(3))(1+sqrt(3))^n/12+(3-sqrt(3))(1-sqrt(3))^n/12+2^((n-4)/2)(1+(-1)^n) a(n)=A002605(n)/2+2^((n-4)/2)(1+(-1)^n).
%Y Cf. A099177.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Oct 02 2004