%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.
%A _Paul Barry_, May 16 2004