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%I #20 Oct 11 2017 05:14:55
%S 9,339,3606,24474,121077,475353,1568712,4524540,11722134,27828138,
%T 61442460,127616970,251577939,474068124,858822579,1502804622,
%U 2549955858,4209357693,6778862319,10675429650,16473604089,24953782251,37162160802,54484513344,78736227726
%N Number of ways to place 5 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.
%C All elements of the sequence are multiples of 3.
%H Heinrich Ludwig, <a href="/A244503/b244503.txt">Table of n, a(n) for n = 4..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F a(n) = 1/3840*n^10 + 1/768*n^9 - 13/384*n^8 - 7/384*n^7 + 1589/768*n^6 - 24619/3840*n^5 - 1561/32*n^4 + 20965/64*n^3 - 11101/240*n^2 - 85143/20*n + 9711 for n >= 7.
%F G.f.: -3*x^4*(5*x^13 - 15*x^12 - 26*x^11 + 228*x^10 - 584*x^9 + 706*x^8 - 162*x^7 - 542*x^6 + 766*x^5 - 924*x^4 + 656*x^3 + 124*x^2 + 80*x + 3) / (x - 1)^11. - _Colin Barker_, Jun 29 2014
%t CoefficientList[Series[-3*(5*x^13 -15*x^12 -26*x^11 +228*x^10 -584*x^9 +706*x^8 -162*x^7 -542*x^6 +766*x^5 -924*x^4 +656*x^3 +124*x^2 +80*x +3) / (x-1)^11, {x, 0, 20}], x] (* _Vaclav Kotesovec_, Jul 03 2014 after _Colin Barker_ *)
%Y Cf. A086274, A244500, A244501, A244502.
%K nonn,easy
%O 4,1
%A _Heinrich Ludwig_, Jun 29 2014
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