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 A283115 #9 Mar 07 2017 00:46:21
%S A283115 0,0,0,0,0,3,40,242,1038,3504,9998,25158,57410,121023,239148,447552,
%T A283115 799764,1373400,2278290,3666036,5742396,8781111,13141326,19287246,
%U A283115 27811906,39463424,55177122,76109826,103681214,139618479,186008654,245354424,320640264,415401264
%N A283115 Number of nonequivalent ways (mod D_3) to place 4 points on an n X n X n triangular grid so that no two of them are on the same row, column or diagonal.
%C A283115 In terms of triangular chess: Number of nonequivalent ways (mod D_3) to arrange 4 nonattacking rooks on an n X n X n board.
%C A283115 Reflections and rotations of placements are not counted. For numbers if they are to be counted see A193982.
%H A283115 Heinrich Ludwig, <a href="/A283115/b283115.txt">Table of n, a(n) for n = 1..1000</a>
%H A283115 <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-6,0,6,8,-12,-9,13,6,-6,-13,9,12,-8,-6,0,6,0,-3,1).
%F A283115 a(n) = (5*n^8 - 100*n^7 + 810*n^6 - 3336*n^5 + 6940*n^4 - 5120*n^3 - 4080*n^2 + 6336*n)/11520 + IF(MOD(n, 2) = 1, 4*n^3 - 38*n^2 + 144*n - 207)/768 + IF(MOD(n, 3) = 1, n^2 - 6*n + 8)/18 + IF(MOD(n, 6) = 1, -1)/6.
%F A283115 G.f.: x^6*(3 + 31*x + 122*x^2 + 330*x^3 + 630*x^4 + 920*x^5 + 1128*x^6 + 1224*x^7 + 1124*x^8 + 924*x^9 + 644*x^10 + 336*x^11 + 117*x^12 + 27*x^13) / ((1 - x)^9*(1 + x)^4*(1 - x + x^2)*(1 + x + x^2)^3). - _Colin Barker_, Mar 01 2017
%e A283115 There are a(6) = 3 ways to place 4 points on an 6 X 6 X 6 grid, rotations and reflections ignored:
%e A283115 . X .
%e A283115 . X . . X .
%e A283115 . . . . . . . . X
%e A283115 . . X . . . X . . . . .
%e A283115 X . . . . . X . . . . X . . .
%e A283115 . . . X . . . . . X . . . . . X . .
%t A283115 Table[(5 n^8 - 100 n^7 + 810 n^6 - 3336 n^5 + 6940 n^4 - 5120 n^3 - 4080 n^2 + 6336 n)/11520 + Boole[OddQ@ n] (4 n^3 - 38 n^2 + 144 n - 207)/768 + Boole[Mod[n, 3] == 1] (n^2 - 6 n + 8)/18 - Boole[Mod[n, 6] == 1]/6, {n, 34}] (* or *)
%t A283115 Rest@ CoefficientList[Series[x^6*(3 + 31 x + 122 x^2 + 330 x^3 + 630 x^4 + 920 x^5 + 1128 x^6 + 1224 x^7 + 1124 x^8 + 924 x^9 + 644 x^10 + 336 x^11 + 117 x^12 + 27 x^13)/((1 - x)^9*(1 + x)^4*(1 - x + x^2) (1 + x + x^2)^3), {x, 0, 34}], x] (* _Michael De Vlieger_, Mar 01 2017 *)
%o A283115 (PARI) concat(vector(5), Vec(x^6*(3 + 31*x + 122*x^2 + 330*x^3 + 630*x^4 + 920*x^5 + 1128*x^6 + 1224*x^7 + 1124*x^8 + 924*x^9 + 644*x^10 + 336*x^11 + 117*x^12 + 27*x^13) / ((1 - x)^9*(1 + x)^4*(1 - x + x^2)*(1 + x + x^2)^3) + O(x^40))) \\ _Colin Barker_, Mar 01 2017
%Y A283115 Cf. A193982, A283113, A283114 (3 points), A283116 (5 points).
%K A283115 nonn,easy
%O A283115 1,6
%A A283115 _Heinrich Ludwig_, Mar 01 2017