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A094632 A trace sequence for a Napoleon graph. 1


%S 1,0,3,4,21,55,198,609,2021,6460,21033,67859,219926,711165,2302233,

%T 7448804,24107061,78008495,252446598,816924969,2643639901,8554973900,

%U 27684516753,89588913979,289915919446,938187455205,3036038652273

%N A trace sequence for a Napoleon graph.

%C a(n)=trace(A^n)/6 where A is the adjacency matrix of the graph obtained by constructing external triangles on the sides of a triangle (or equivalently, taking a triangle and its midpoint triangle). A Lucas Jacobsthal product. Compare with A093042.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,7,2,-4).

%F G.f. : (1-x-4x^2-x^3)/((1-2x-4x^2)(1+x-x^2)); a(n)=L(n)*A078008(n)/2=A000034(n)*A078008(n)/2.

%K easy,nonn

%O 0,3

%A _Paul Barry_, May 16 2004

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Last modified April 1 13:11 EDT 2020. Contains 333159 sequences. (Running on oeis4.)