cp's OEIS Frontend

A240441 Number of ways to place 4 points on a triangular grid of side n so that no three of these points are vertices of an equilateral triangle of any orientation.

%I A240441 #15 Oct 10 2017 22:33:53
%S A240441 0,0,3,114,969,4773,17415,52125,135375,315675,676200,1352085,2553558,
%T A240441 4595934,7937874,13229118,21369330,33579450,51487425,77229900,
%U A240441 113571975,164046795,233117313,326362179,450688329,614572413,828333870,1104441975,1457859900,1906428300
%N A240441 Number of ways to place 4 points on a triangular grid of side n so that no three of these points are vertices of an equilateral triangle of any orientation.
%H A240441 Heinrich Ludwig, <a href="/A240441/b240441.txt">Table of n, a(n) for n = 1..1000</a>
%H A240441 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (7,-19,21,6,-42,42,-6,-21,19,-7,1).
%F A240441 a(n) = (n^8 + 4*n^7 - 14*n^6 - 56*n^5 + 61*n^4 + 220*n^3 - 84*n^2 - 240*n)/384 + IF(MOD(n, 2) = 1)*(6*n + 3)/32.
%F A240441 G.f.: -3*x^3*(x^4+31*x^3+76*x^2+31*x+1) / ((x-1)^9*(x+1)^2). - _Colin Barker_, Apr 05 2014
%t A240441 Table[(n^8+4*n^7-14*n^6-56*n^5+61*n^4+220*n^3-84*n^2-240*n)/384 +If[EvenQ[n],0,(6*n+3)/32],{n,1,20}] (* _Vaclav Kotesovec_, Apr 05 2014 after _Heinrich Ludwig_ *)
%o A240441 (PARI) concat([0,0], Vec(-3*x^3*(x^4+31*x^3+76*x^2+31*x+1)/((x-1)^9*(x+1)^2) + O(x^100))) \\ _Colin Barker_, Apr 05 2014
%Y A240441 Cf. A240439, A240440, A240442.
%K A240441 nonn,easy
%O A240441 1,3
%A A240441 _Heinrich Ludwig_, Apr 05 2014