Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #5 Jun 13 2015 00:51:21
%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