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%I #9 Sep 12 2015 11:00:18
%S 0,0,0,0,0,0,4,94,550,2292,7552,21362,52856,117694,241484,463038,
%T 838816,1448002,2398292,3832374,5935120,8941514,13145292,18908302,
%U 26670584,36961170,50409604,67758182,89874912,117767194,152596220
%N Number of ways to place 6 nonattacking queens on a 6 X n board.
%H Vincenzo Librandi, <a href="/A061992/b061992.txt">Table of n, a(n) for n = 0..1000</a>
%H Vaclav Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Number of ways of placing non-attacking queens and kings on boards of various sizes</a>, part of V. Kotesovec, Between chessboard and computer, 1996, pp. 204 - 206.
%F G.f.: - 2*x^6*(4*x^17 - 12*x^16 + 12*x^15 + 10*x^14 - 10*x^13 + 40*x^12 - 278*x^11 + 677*x^10 - 582*x^9 - 62*x^8 + 654*x^7 - 501*x^6 + 293*x^5 - 46*x^4 + 138*x^3 - 12*x^2 + 33*x + 2)/(x - 1)^7.
%F 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 >= 24.
%F Explicit formula (V.Kotesovec, 1992): a(n) = n^6 - 45*n^5 + 943*n^4 - 11755*n^3 + 91480*n^2 - 418390*n + 870920, n >= 17.
%t CoefficientList[Series[-2 x^6 (4 x^17 -12 x^16 + 12 x^15 + 10 x^14 - 10 x^13 + 40 x^12 - 278 x^11 + 677 x^10 - 582 x^9 - 62 x^8 + 654 x^7 - 501 x^6 + 293 x^5 - 46 x^4 + 138 x^3 - 12 x^2 + 33 x + 2) / (x-1)^7, {x, 0, 40}], x] (* _Vincenzo Librandi_, May 12 2013 *)
%Y Cf. A061989, A061990, A061991.
%K nonn,easy
%O 0,7
%A Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), May 31 2001
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