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 A061593 Number of ways to place 2n nonattacking kings on a 4 X 2n chessboard. 10
 12, 79, 408, 1847, 7698, 30319, 114606, 419933, 1501674, 5266069, 18174084, 61892669, 208424880, 695179339, 2299608732, 7552444115, 24648046806, 79994460139, 258339007890, 830619734681, 2660070154542, 8488515938929, 27000079296648, 85629004867577 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Bruno Berselli, Table of n, a(n) for n = 1..200 V. Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 90. D. E. Knuth, Nonattacking kings on a chessboard, 1994. H. S. Wilf, The problem of the kings, Elec. J. Combin. 2, 1995. Index entries for linear recurrences with constant coefficients, signature (9,-28,33,-9). FORMULA 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). a(n) = 17*A027471(n+2)-126*A000244(n)+A025169(n+4). MAPLE with(combinat): A061593:=n->(17*n-109)*3^n+2*fibonacci(2*n+10): seq(A061593(n), n=1..30); # Wesley Ivan Hurt, Nov 08 2014 MATHEMATICA Table[(17 n - 109)*3^n + 2 Fibonacci[2 n + 10], {n, 30}] (* Wesley Ivan Hurt, Nov 08 2014 *) PROG (MAGMA) [(17*n-109)*3^n+2*Fibonacci(2*n+10): n in [1..30]]; // Vincenzo Librandi, Jul 12 2011 CROSSREFS Cf. A061594, A001787. Sequence in context: A224775 A258480 A035042 * A243955 A232044 A190216 Adjacent sequences:  A061590 A061591 A061592 * A061594 A061595 A061596 KEYWORD nonn,easy,nice AUTHOR Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), May 22 2001 STATUS approved

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Last modified December 18 20:06 EST 2018. Contains 318245 sequences. (Running on oeis4.)