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A099177 a(n)=2a(n-1)+4a(n-2)-4a(n-3)-4a(n-4). 4

%I

%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

%Y Cf. A099176.

%K easy,nonn

%O 0,3

%A _Paul Barry_, Oct 02 2004

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Last modified January 24 01:05 EST 2020. Contains 331178 sequences. (Running on oeis4.)