A094632 A trace sequence for a Napoleon graph.

1, 0, 3, 4, 21, 55, 198, 609, 2021, 6460, 21033, 67859, 219926, 711165, 2302233, 7448804, 24107061, 78008495, 252446598, 816924969, 2643639901, 8554973900, 27684516753, 89588913979, 289915919446, 938187455205, 3036038652273

Offset

0,3

Comments

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.

Links

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (1,7,2,-4).

Formula

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.

Crossrefs

Sequence in context: A254884 A034475 A156173 * A081698 A182096 A012123

Adjacent sequences: A094629 A094630 A094631 * A094633 A094634 A094635

Keyword

easy,nonn

Author

Paul Barry, May 16 2004

Status

approved