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 A061996 Number of ways to place 3 nonattacking kings on an n X n board. 19
 0, 0, 0, 8, 140, 964, 3920, 11860, 29708, 65240, 129984, 240240, 418220, 693308, 1103440, 1696604, 2532460, 3684080, 5239808, 7305240, 10005324, 13486580, 17919440, 23500708, 30456140, 39043144, 49553600, 62316800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Vaclav Kotesovec, Placing non-attacking queens and kings on boards of various sizes, part of "Between chessboard and computer", 1996, pp. 204 - 206. Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1). FORMULA G.f.: 4*x^3*(2 + 21*x + 38*x^2 - 42*x^3 + 11*x^4)/(1 - x)^7. Recurrence: a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7), n >= 8. a(n) = (n-1)*(n-2)*(n^4 + 3*n^3 - 20*n^2 - 30*n + 132)/6, n >= 1. a(n) = A193580(n,3). - R. J. Mathar, Sep 03 2016 E.g.f.: -44 + (1/6)*(264 -264*x +132*x^2 -36*x^3 +38*x^4 +15*x^5 +x^6)*exp(x). - G. C. Greubel, Apr 29 2022 MATHEMATICA CoefficientList[Series[4x^3(2 +21x +38x^2 -42x^3 +11x^4)/(1-x)^7, {x, 0, 40}], x] (* Vincenzo Librandi, May 02 2013 *) PROG (SageMath) [(n-1)*(n-2)*(n^4+3*n^3-20*n^2-30*n+132)/6 -44*bool(n==0) for n in (0..40)] # G. C. Greubel, Apr 29 2022 CROSSREFS Cf. A061995, A061997, A061998, A193580. Sequence in context: A301835 A091060 A201094 * A345650 A092703 A234353 Adjacent sequences: A061993 A061994 A061995 * A061997 A061998 A061999 KEYWORD nonn,easy AUTHOR Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), May 31 2001 STATUS approved

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Last modified September 10 06:02 EDT 2024. Contains 375773 sequences. (Running on oeis4.)