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%I #17 Oct 11 2017 05:11:17
%S 1,8,55,248,820,2212,5163,10815,20833,37540,64067,104518,164150,
%T 249568,368935,532197,751323,1040560,1416703,1899380,2511352,3278828,
%U 4231795,5404363,6835125,8567532,10650283,13137730,16090298,19574920,23665487,28443313,33997615
%N Number of ways to place 3 points on an n X n X n triangular grid so that no pair of them has distance sqrt(3).
%C sqrt(3) is the second closest (Euclidean) distance for a pair of points in a triangular grid. For illustration see A244500.
%H Heinrich Ludwig, <a href="/A244501/b244501.txt">Table of n, a(n) for n = 2..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F a(n) = 1/48*n^6 + 1/16*n^5 - 13/16*n^4 + 61/48*n^3 + 247/24*n^2 - 293/6*n + 6 for n >= 3.
%F G.f.: -x^2*(6*x^7 - 17*x^6 + 14*x^5 - 6*x^4 - 4*x^3 + 20*x^2 + x + 1) / (x-1)^7. - _Colin Barker_, Jun 29 2014
%t CoefficientList[Series[-(6*x^7-17*x^6+14*x^5-6*x^4-4*x^3+20*x^2+x+1) / (x-1)^7, {x, 0, 20}], x] (* _Vaclav Kotesovec_, Jul 03 2014 after _Colin Barker_ *)
%o (PARI) Vec(-x^2*(6*x^7-17*x^6+14*x^5-6*x^4-4*x^3+20*x^2+x+1)/(x-1)^7 + O(x^100)) \\ _Colin Barker_, Jun 29 2014
%Y Cf. A086274, A244500, A244502, A244503.
%K nonn,easy
%O 2,2
%A _Heinrich Ludwig_, Jun 29 2014