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A100305 Expansion of (1-x-4x^2)/(1-2x-7x^2+8x^3). 1


%S 1,1,5,9,45,113,469,1369,5117,16065,56997,185513,641485,2125585,

%T 7257461,24262137,82321821,276418913,934993477,3146344777,10626292589,

%U 35797050801,120807391509,407183797913,1373642929981,4631113313281

%N Expansion of (1-x-4x^2)/(1-2x-7x^2+8x^3).

%C Construct a graph as follows:form the graph whose adjacency matrix is the tensor product of that of P_3 and [1,1;1,1], then add a loop at each of the 'internal' nodes. (Spectrum : [0^3;1;(1-sqrt(33))/2;(1+sqrt(33))/2]). a(n) counts closed walks of length n at each of the 'internal' nodes. Partial sums of A100303.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2, 7, -8).

%F a(n)=2a(n-1)+7a(n-2)-8a(n-3); a(n)=1/2+((sqrt(33)+1)^(n+1)+(sqrt(33)-1)^(n+1)(-1)^n)sqrt(33)2^(-n)/132.

%t CoefficientList[Series[(1-x-4x^2)/(1-2x-7x^2+8x^3),{x,0,40}],x] (* or *) LinearRecurrence[{2,7,-8},{1,1,5},40] (* _Harvey P. Dale_, Oct 05 2012 *)

%Y Cf. A100304.

%K easy,nonn

%O 0,3

%A _Paul Barry_, Nov 12 2004

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Last modified January 28 04:30 EST 2022. Contains 350654 sequences. (Running on oeis4.)