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 A279440 #13 Dec 24 2016 09:39:33
%S A279440 0,0,6,2040,71400,1005720,8421630,50092896,233483040,905925600,
%T A279440 3045791430,9125544120,24868110696,62593429080,147255640350,
%U A279440 326843422080,689604309120,1391614736256,2699616160710,5055848825400,9173923662120,16177675640280,27798546316926,46651469520480
%N A279440 Number of ways to place 6 points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.
%C A279440 Column 7 of triangle A279445.
%C A279440 Rotations and reflections of placements are counted. For numbers if they are to be ignored see A279450.
%C A279440 For condition "no more than 2 points on straight lines at any angle", see A194191.
%H A279440 Heinrich Ludwig, <a href="/A279440/b279440.txt">Table of n, a(n) for n = 1..1000</a>
%H A279440 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F A279440 a(n) = (n^12 -55*n^10 +210*n^9 +93*n^8 -2220*n^7 +5855*n^6 -7350*n^5 +4786*n^4 -1440*n^3 +120*n^2)/720.
%F A279440 a(n) = 13*a(n-1) -78*a(n-2) +286*a(n-3) -715*a(n-4) +1287*a(n-5) -1716*a(n-6) +1716*a(n-7) -1287*a(n-8) +715*a(n-9) -286*a(n-10) +78*a(n-11) -13*a(n-12) +*a(n-13).
%F A279440 G.f.: 6*x^3*(1 +327*x +7558*x^2 +39154*x^3 +56220*x^4 +14724*x^5 -6262*x^6 -978*x^7 +131*x^8 +5*x^9) / (1 -x)^13. - _Colin Barker_, Dec 22 2016
%t A279440 Table[(n^12 - 55 n^10 + 210 n^9 + 93 n^8 - 2220 n^7 + 5855 n^6 - 7350 n^5 + 4786 n^4 - 1440 n^3 + 120 n^2)/720, {n, 24}] (* or *)
%t A279440 Rest@ CoefficientList[Series[6 x^3 (1 + 327 x + 7558 x^2 + 39154 x^3 + 56220 x^4 + 14724 x^5 - 6262 x^6 - 978 x^7 + 131 x^8 + 5 x^9)/(1 - x)^13, {x, 0, 24}], x] (* _Michael De Vlieger_, Dec 22 2016 *)
%o A279440 (PARI) concat(vector(2), Vec(6*x^3*(1 +327*x +7558*x^2 +39154*x^3 +56220*x^4 +14724*x^5 -6262*x^6 -978*x^7 +131*x^8 +5*x^9) / (1 -x)^13 + O(x^30))) \\ _Colin Barker_, Dec 22 2016
%Y A279440 Cf. A194191, A279450, A279444, A279445, A197458.
%Y A279440 Same problem but 2..5,7,8,9 points: A083374, A279437, A279438, A279439, A279441, A279442, A279443.
%K A279440 nonn,easy
%O A279440 1,3
%A A279440 _Heinrich Ludwig_, Dec 22 2016