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A061593
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Number of ways to place 2n nonattacking kings on a 4 X 2n chessboard.
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13
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12, 79, 408, 1847, 7698, 30319, 114606, 419933, 1501674, 5266069, 18174084, 61892669, 208424880, 695179339, 2299608732, 7552444115, 24648046806, 79994460139, 258339007890, 830619734681, 2660070154542, 8488515938929, 27000079296648, 85629004867577
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OFFSET
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1,1
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LINKS
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FORMULA
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G.f.: x*(12-29*x+33*x^2-9*x^3)/((1-3*x+x^2)*(1-3*x)^2).
a(n) = 9*a(n-1) - 28*a(n-2) + 33*a(n-3) - 9*a(n-4); a(1)=12, a(2)=79, a(3)=408, a(4)=1847.
a(n) = (17*n-109)*3^n + 2*Fibonacci(2*n+10).
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MAPLE
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MATHEMATICA
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Table[(17 n - 109)*3^n + 2 Fibonacci[2 n + 10], {n, 30}] (* Wesley Ivan Hurt, Nov 08 2014 *)
CoefficientList[Series[x (12-29x+33x^2-9x^3)/((1-3x+x^2)(1-3x)^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{9, -28, 33, -9}, {0, 12, 79, 408, 1847}, 30] (* Harvey P. Dale, Dec 20 2021 *)
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PROG
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(Magma) [(17*n-109)*3^n+2*Fibonacci(2*n+10): n in [1..30]]; // Vincenzo Librandi, Jul 12 2011
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), May 22 2001
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STATUS
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approved
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