A231654 - OEIS

%I #19 Feb 10 2024 09:22:38

%S 0,0,2,48,526,3450,16536,63104,204202,580669,1491096,3520768,7754502,

%T 16098425,31770760,59998736,109022244,191454654,326158974,540703008,

%U 874630262,1383621756,2144889472,3263884272,4882793214,7190910467,10437526372,14947411024

%N Number of non-equivalent ways to choose 5 points in an equilateral triangle grid of side n.

%H Heinrich Ludwig, <a href="/A231654/b231654.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (6,-10,-10,50,-34,-66,110,0,-110,66,34,-50,10,10,-6,1).

%F a(n) = (n^10 + 5*n^9 - 10*n^8 - 70*n^7 + 25*n^6 + 584*n^5 - 420*n^4 - 480*n^3 - 1216*n^2 + 1536*n + B)/23040 where B = 375*n^4 - 1170*n^3 + 210*n^2 - 405*n + 1035 if n odd, and B = 0 if n even.

%F G.f.: x^3*(x^11 -4*x^10 +14*x^9 -78*x^8 -189*x^7 -902*x^6 -1316*x^5 -1476*x^4 -794*x^3 -258*x^2 -36*x -2) / ((x -1)^11*(x +1)^5). - _Colin Barker_, Feb 15 2014

%t Table[If[EvenQ[n], b = 0, b = 375*n^4 - 1170*n^3 + 210*n^2 - 405*n + 1035]; (n^10 + 5*n^9 - 10*n^8 - 70*n^7 + 25*n^6 + 584*n^5 - 420*n^4 - 480*n^3 - 1216*n^2 + 1536*n + b)/23040, {n, 30}] (* _T. D. Noe_, Nov 14 2013 *)

%Y Cf. A001399, A227327, A230723, A231653, A231655.

%K nonn,easy

%O 1,3

%A _Heinrich Ludwig_, Nov 13 2013