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A069361
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Number of 3 X n binary arrays with a path of adjacent 1's from top row to bottom row.
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94
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1, 17, 197, 1985, 18621, 167337, 1461797, 12519345, 105683341, 882516857, 7308428597, 60131384705, 492202181661, 4012347269577, 32599584662597, 264152863210065, 2135714594033581, 17236446198921497, 138901692341235797, 1117982939085627425, 8989229069675479101
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OFFSET
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1,2
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LINKS
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FORMULA
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From Maksym Voznyy (voznyy(AT)mail.ru), Jul 25 2008: (Start)
a(n) = 15*a(n-1) - 58*a(n-2) + 16*a(n-3), where a(1)=1, a(2)=17, a(3)=197;
a(n) = 8^n + 1/sqrt(41)*4^(n+1)*((7+sqrt(41))^(-(n+1)) - (7-sqrt(41))^(-(n+1))). (End)
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EXAMPLE
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The 17 binary arrays for n=2:
01 10 01 10 01 10 01 10 01 10 11 11 11 11 11 11 11
01 10 01 10 11 11 11 11 11 11 01 10 01 01 11 11 11
01 10 11 11 01 10 10 01 11 11 01 10 11 11 01 10 11 - R. J. Mathar, Jun 21 2023
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MATHEMATICA
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PROG
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(PARI) x='x+O('x^30); Vec(x*(1+2*x)/((1-8*x)*(2*x^2-7*x+1))) \\ G. C. Greubel, Apr 22 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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