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%I #8 Feb 12 2023 16:03:33
%S 0,1,2,8,20,60,160,448,1216,3344,9120,24960,68160,186304,508928,
%T 1390592,3799040,10379520,28357120,77473792,211661824,578272256,
%U 1579868160,4316282880,11792302080,32217174016,88018952192,240472260608
%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 A099177 counts walks of length n between 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.: x/((1-2x^2)(1-2x-2x^2)); 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).
%F a(n)=sum{k=0..floor((n+1)/2), binomial(n-k+1, k-1)2^(n-k)} - _Paul Barry_, Oct 23 2004
%t LinearRecurrence[{2,4,-4,-4},{0,1,2,8},30] (* _Harvey P. Dale_, Feb 12 2023 *)
%Y Cf. A099176.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Oct 02 2004
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