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 A279446 #13 Mar 07 2017 00:45:54
%S A279446 0,0,1,66,2096,25676,187984,983172,4073312,14196011,43309138,
%T A279446 118818916,298926225,699619679,1540212590,3217045155,6419240369,
%U A279446 12304959047,22763742133,40797668697,71065355815,120643462032,200077436639,324808463585,517088445952,808515893580
%N A279446 Number of non-equivalent (mod D_3) ways to place 6 indistinguishable points on a triangular grid of side n so that no two of them are adjacent.
%C A279446 Rotations and reflections of placements are not counted. For numbers if they are to be counted see A282998.
%H A279446 Heinrich Ludwig, <a href="/A279446/b279446.txt">Table of n, a(n) for n = 3..1000</a>
%H A279446 <a href="/index/Rec#order_25">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,-17,8,36,-7,-68,-18,113,52,-126,-92,92,126,-52,-113,18,68,7,-36,-8,17,0,-4,1).
%F A279446 a(n) = (n^12 + 6*n^11 - 195*n^10 - 670*n^9 + 17455*n^8 + 13426*n^7 - 835256*n^6 + 1246240*n^5 + 19563664*n^4 - 68181792*n^3 - 131524224*n^2 + 969500160*n - 1298903040)/276480 + IF(MOD(n, 2) = 1, 162*n^5 - 715*n^4 - 4480*n^3 + 21955*n^2 + 1108*n - 41685)/30720 + IF(MOD(n, 3) = 1, n^2 + n - 25)/27 for n>=4.
%F A279446 G.f.: x^5*(1 + 62*x + 1832*x^2 + 17309*x^3 + 86394*x^4 + 266304*x^5 + 557979*x^6 + 818157*x^7 + 829988*x^8 + 519203*x^9 + 94134*x^10 - 150065*x^11 - 123434*x^12 + 7445*x^13 + 64052*x^14 + 29943*x^15 - 11247*x^16 - 15803*x^17 - 3012*x^18 + 3100*x^19 + 1722*x^20 - 15*x^21 - 233*x^22 - 56*x^23) / ((1 - x)^13*(1 + x)^6*(1 + x + x^2)^3). - _Colin Barker_, Feb 26 2017
%e A279446 There is a(5) = 1 way to place 6 points on a triangular grid of side n = 5:
%e A279446 X
%e A279446 . .
%e A279446 X . X
%e A279446 . . . .
%e A279446 X . X . X
%t A279446 Table[Boole[n > 4] ((n^12 + 6 n^11 - 195 n^10 - 670 n^9 + 17455 n^8 + 13426 n^7 - 835256 n^6 + 1246240 n^5 + 19563664 n^4 - 68181792 n^3 - 131524224 n^2 + 969500160 n - 1298903040)/276480 + Boole[OddQ@ n] (162 n^5 - 715 n^4 - 4480 n^3 + 21955 n^2 + 1108 n - 41685)/30720 + Boole[Mod[n, 3] == 1] (n^2 + n - 25)/27), {n, 3, 28}] (* _Michael De Vlieger_, Feb 26 2017 *)
%o A279446 (PARI) concat(vector(2), Vec(x^5*(1 + 62*x + 1832*x^2 + 17309*x^3 + 86394*x^4 + 266304*x^5 + 557979*x^6 + 818157*x^7 + 829988*x^8 + 519203*x^9 + 94134*x^10 - 150065*x^11 - 123434*x^12 + 7445*x^13 + 64052*x^14 + 29943*x^15 - 11247*x^16 - 15803*x^17 - 3012*x^18 + 3100*x^19 + 1722*x^20 - 15*x^21 - 233*x^22 - 56*x^23) / ((1 - x)^13*(1 + x)^6*(1 + x + x^2)^3) + O(x^30))) \\ _Colin Barker_, Feb 26 2017
%Y A279446 Cf. A282998, A239572, A032091 (2 points), A239573 (3 points), A239574 (4 points), A239575 (5 points).
%K A279446 nonn,easy
%O A279446 3,4
%A A279446 _Heinrich Ludwig_, Feb 26 2017