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A093121
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A Jacobsthal Fibonacci product.
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1
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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
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0,3
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COMMENTS
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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.
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LINKS
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FORMULA
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G.f.: (1-x-3x^2)/((1+x-x^2)(1-2x-4x^2));
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)).
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MATHEMATICA
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LinearRecurrence[{1, 7, 2, -4}, {1, 0, 4, 6}, 30] (* Harvey P. Dale, Aug 26 2019 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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