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%I #23 Sep 08 2022 08:45:03
%S 0,0,0,16,78,228,520,1020,1806,2968,4608,6840,9790,13596,18408,24388,
%T 31710,40560,51136,63648,78318,95380,115080,137676,163438,192648,
%U 225600,262600,303966,350028,401128,457620,519870,588256
%N Number of ways to place 2 nonattacking kings on an n X n board.
%H Vincenzo Librandi, <a href="/A061995/b061995.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.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1)
%F G.f.: 2*x^3*(x^2 + x - 8)/(x - 1)^5.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5), n >= 6.
%F a(n) = (n - 1)*(n - 2)*(n^2 + 3*n - 2)/2, n >= 1.
%F E.g.f.: (4 - (4 - 4*x + 2*x^2 - 6*x^3 - x^4)*exp(x))/2. - _G. C. Greubel_, Nov 04 2018
%t CoefficientList[Series[2 x^3 (-8 + x + x^2) / (x-1)^5, {x, 0, 40}], x] (* _Vincenzo Librandi_, May 02 2013 *)
%o (PARI) x='x+O('x^30); Vec(2*x^3*(x^2+x-8)/(x-1)^5) \\ _G. C. Greubel_, Nov 04 2018
%o (Magma) [0] cat [(n-1)*(n-2)*(n^2+3*n-2)/2: n in [1..30]]; // _G. C. Greubel_, Nov 04 2018
%Y Cf. A061996, A061997, A061998.
%K nonn,easy
%O 0,4
%A Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), May 31 2001
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