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A069294
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Number of n X 3 binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.
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27
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12, 110, 926, 7556, 60920, 488860, 3915640, 31340216, 250769592, 2006308480, 16050948896, 128409116176, 1027277763840, 8218237436320, 65745948074080, 525967738606656, 4207742397091072, 33661940724484800, 269295530702399616
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OFFSET
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2,1
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LINKS
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FORMULA
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G.f.: 2*x^2*(6-17*x+7*x^2+8*x^3)/(1-8*x)/(2*x^3+2*x^2-4*x+1). - Vladeta Jovovic, Jul 02 2003
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MATHEMATICA
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LinearRecurrence[{12, -34, 14, 16}, {12, 110, 926, 7556}, 50] (* G. C. Greubel, Apr 22 2018 *)
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PROG
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(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 16, 14, -34, 12]^(n-2)*[12; 110; 926; 7556])[1, 1] \\ Charles R Greathouse IV, May 10 2016
(PARI) x='x+O('x^30); Vec(2*x^2*(6-17*x+7*x^2+8*x^3)/((1-8*x)*(2*x^3 +2*x^2-4*x+1))) \\ G. C. Greubel, Apr 22 2018
(Magma) I:=[12, 110, 926, 7556]; [n le 4 select I[n] else 12*Self(n-1) - 34*Self(n-2) +14*Self(n-3) + 16*Self(n-4): n in [1..30]]; // G. C. Greubel, Apr 22 2018
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CROSSREFS
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Cf. n X 2 A002450, n X 4 A069295, n X 5 A069296, n X 6 A069297, n X 7 A069298, n X 8 A069299, n X 9 A069300, n X 10 A069301, n X 11 A069302, n X 12 A069303, n X 13 A069304, n X 14 A069305, read by rows A069306-A069320.
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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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