This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A279112 #16 Dec 21 2016 12:16:38
%S A279112 0,0,2,20,138,505,1547,3759,8313,16350,30344,52470,87212,138255,
%T A279112 212953,317065,461827,655724,915038,1251720,1688414,2241365,2941047,
%U A279112 3808915,4884893,6196650,7795332,9715914,12022688,14759115,18004709,21812685,26280007,31471000,37502458
%N A279112 Number of non-equivalent ways to place 3 non-attacking kings on an n X n board.
%C A279112 Rotations and reflections of placements are not counted. If they are to be counted, see A061996.
%H A279112 Heinrich Ludwig, <a href="/A279112/b279112.txt">Table of n, a(n) for n = 1..1000</a>
%H A279112 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-11,6,14,-14,-6,11,-1,-3,1).
%F A279112 a(n) = (n^6 - 27*n^4 + 44*n^3 + 146*n^2 - 404*n + 240 + IF(MOD(n, 2) = 1, 8*n^3 - 21*n^2 + 16*n - 51))/48 for n >=2.
%F A279112 a(n) = 3*a(n-1) + a(n-2) - 11*a(n-3) + 6*a(n-4) + 14*a(n-5) - 14*a(n-6) - 6*a(n-7) + 11*a(n-8) - a(n-9) - 3*a(n-10) + a(n-11).
%F A279112 From _Colin Barker_, Dec 07 2016: (Start)
%F A279112 a(n) = (n^6 - 27*n^4 + 44*n^3 + 146*n^2 - 404*n + 240)/48 for n>1.
%F A279112 a(n) = (n^6 - 27*n^4 + 52*n^3 + 125*n^2 - 388*n + 189)/48 for n>1.
%F A279112 G.f.: x^3*(2 + 14*x + 76*x^2 + 93*x^3 + 102*x^4 - 17*x^5 - 36*x^6 - x^7 + 8*x^8 - x^9) / ((1 - x)^7*(1 + x)^4).
%F A279112 (End)
%e A279112 There are 2 non-equivalent ways to place 3 non-attacking kings on a 3 X 3 board:
%e A279112 K.K K.K
%e A279112 ... ...
%e A279112 ..K .K.
%t A279112 Table[Boole[n > 1] (n^6 - 27 n^4 + 44 n^3 + 146 n^2 - 404 n + 240 + Boole[OddQ@ n] (8 n^3 - 21 n^2 + 16 n - 51))/48, {n, 35}] (* or *)
%t A279112 Rest@ CoefficientList[Series[x^3*(2 + 14 x + 76 x^2 + 93 x^3 + 102 x^4 - 17 x^5 - 36 x^6 - x^7 + 8 x^8 - x^9)/((1 - x)^7*(1 + x)^4), {x, 0, 35}], x] (* _Michael De Vlieger_, Dec 08 2016 *)
%o A279112 (PARI) concat(vector(2), Vec(x^3*(2 + 14*x + 76*x^2 + 93*x^3 + 102*x^4 - 17*x^5 - 36*x^6 - x^7 + 8*x^8 - x^9) / ((1 - x)^7*(1 + x)^4) + O(x^60))) \\ _Colin Barker_, Dec 07 2016
%Y A279112 Cf. A061996, A279111 (2 kings), A279113 (4 kings), A279114 (5 kings), A279115 (6 kings), A279116 (7 kings), A279117, A236679.
%K A279112 nonn,easy
%O A279112 1,3
%A A279112 _Heinrich Ludwig_, Dec 07 2016