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 A243143 #18 Feb 26 2025 01:59:37
%S A243143 1,22,170,816,2947,8765,22703,52823,113042,225817,426299,766905,
%T A243143 1324282,2206478,3563770,5599258,8584775,12875840,18934040,27347390,
%U A243143 38860741,54402707,75125825,102441321,138070912,184090795,242997153,317760863,411908932,529591532,675681764
%N A243143 Number of inequivalent (mod D_3) ways to place 4 points on a triangular grid of side n so that they are not vertices of an equilateral triangle of any orientation.
%H A243143 Heinrich Ludwig, <a href="/A243143/b243143.txt">Table of n, a(n) for n = 3..1000</a>
%H A243143 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (5,-7,-5,23,-19,-7,27,-27,7,19,-23,5,7,-5,1).
%F A243143 a(n) = (n^8 + 4*n^7 - 14*n^6 - 56*n^5 + 136*n^4 - 104*n^3 + 552*n^2 - 672*n)/2304 + IF(MOD(n, 2) = 1)*(28*n^3 - 198*n^2 + 296*n + 21)/768 + IF(MOD(n-1, 4) <= 1)*(-1/8).
%F A243143 G.f.: -x^3*(3*x^10 -10*x^9 +19*x^8 -13*x^7 +102*x^6 +105*x^5 +144*x^4 +125*x^3 +67*x^2 +17*x +1) / ((x -1)^9*(x +1)^4*(x^2 +1)). - _Colin Barker_, May 30 2014
%t A243143 Drop[CoefficientList[Series[-x^3*(3*x^10 - 10*x^9 + 19*x^8 - 13*x^7 + 102*x^6 + 105*x^5 + 144*x^4 + 125*x^3 + 67*x^2 + 17*x + 1) / ((x-1)^9*(x+1)^4*(x^2+1)), {x, 0, 40}], x],3] (* _Vaclav Kotesovec_, May 31 2014 after _Colin Barker_ *)
%Y A243143 Cf. A243141, A240441, A001399, A227327, A243142, A243144.
%K A243143 nonn,easy
%O A243143 3,2
%A A243143 _Heinrich Ludwig_, May 30 2014