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A094632 A trace sequence for a Napoleon graph. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 21 18:05 EST 2020. Contains 332107 sequences. (Running on oeis4.)