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%I #15 Aug 04 2024 16:44:10
%S 0,0,0,48,600,3108,10388,27328,61668,124900,233288,409008,681408,
%T 1088388,1677900,2509568,3656428,5206788,7266208,9959600,13433448,
%U 17858148,23430468,30376128,38952500,49451428,62202168,77574448,95981648,117884100
%N Number of ways to place 3 nonattacking kings on an n X n toroidal board.
%H Vincenzo Librandi, <a href="/A179404/b179404.txt">Table of n, a(n) for n = 1..1000</a>
%H V. 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>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F Explicit formula: a(n) = 1/6*n^2*(n^4 -27*n^2 +194), n>=4.
%F 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.
%t 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 *)
%t 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 *)
%Y Cf. A061996, A179403.
%K nonn,easy
%O 1,4
%A _Vaclav Kotesovec_, Jan 07 2011
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