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A099176 a(n)=2a(n-1)+4a(n-2)-4a(n-3)-4a(n-4). 2

%I

%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

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Last modified June 4 17:50 EDT 2020. Contains 334828 sequences. (Running on oeis4.)