A093121 - OEIS

A093121

A Jacobsthal Fibonacci product.

1, 0, 4, 6, 30, 80, 286, 882, 2924, 9350, 30438, 98208, 318278, 1029210, 3331820, 10780014, 34888062, 112894960, 365344142, 1182264930, 3825911596, 12380874550, 40065409014, 129654294336, 419570260150, 1357757640330

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OFFSET

0,3

COMMENTS

Form a graph from a triangle and its midpoint triangle. A093121 counts closed walks of length n at a vertex of the midpoint triangle in this configuration.

LINKS

Table of n, a(n) for n=0..25.

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

FORMULA

G.f.: (1-x-3x^2)/((1+x-x^2)(1-2x-4x^2));

a(n)=A078008(n)*A000045(n+1);

a(n)=(2^n/3+2(-1)^n/3)(((1+sqrt(5))/2)^(n+1)/sqrt(5)-((1-sqrt(5))/2)^(n+1)/sqrt(5)).

MATHEMATICA

LinearRecurrence[{1, 7, 2, -4}, {1, 0, 4, 6}, 30] (* Harvey P. Dale, Aug 26 2019 *)

CROSSREFS

Sequence in context: A090530 A154667 A376482 * A248048 A209298 A075590

Adjacent sequences: A093118 A093119 A093120 * A093122 A093123 A093124

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 22 2004

STATUS

approved