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 A179404 Number of ways to place 3 nonattacking kings on an n X n toroidal board. 8
 0, 0, 0, 48, 600, 3108, 10388, 27328, 61668, 124900, 233288, 409008, 681408, 1088388, 1677900, 2509568, 3656428, 5206788, 7266208, 9959600, 13433448, 17858148, 23430468, 30376128, 38952500, 49451428, 62202168, 77574448, 95981648, 117884100 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1). FORMULA Explicit formula: a(n) = 1/6*n^2*(n^4 -27*n^2 +194), n>=4. G.f.: -4*x^4*(12*x^6 -67*x^5 +140*x^4 -112*x^3 -21*x^2 +66*x +12)/(x-1)^7. MATHEMATICA CoefficientList[Series[- 4 x^3 (12 x^6 - 67 x^5 + 140 x^4 - 112 x^3 - 21 x^2 + 66 x + 12) / (x - 1)^7, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 01 2013 *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 0, 48, 600, 3108, 10388, 27328, 61668, 124900}, 30] (* Harvey P. Dale, Aug 04 2024 *) CROSSREFS Cf. A061996, A179403. Sequence in context: A352847 A042949 A190601 * A171343 A151624 A187611 Adjacent sequences: A179401 A179402 A179403 * A179405 A179406 A179407 KEYWORD nonn,easy,changed AUTHOR Vaclav Kotesovec, Jan 07 2011 STATUS approved

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Last modified August 13 07:12 EDT 2024. Contains 375113 sequences. (Running on oeis4.)