A243718 - OEIS

%I #8 Jun 13 2015 00:55:03

%S 1,9,40,195,618,1751,4075,8794,17015,31268,53666,88781,140200,215405,

%T 320013,465436,659965,920114,1257580,1695303,2249206,2950131,3819135,

%U 4896590,6209683,7810096,9732230,12041009,14779220,18027113,21837121,26307056,31500345

%N Number of inequivalent (mod D_8) ways to place 3 nonattacking knights on an n X n board.

%H Heinrich Ludwig, <a href="/A243718/b243718.txt">Table of n, a(n) for n = 2..1000</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-11,6,14,-14,-6,11,-1,-3,1).

%F a(n) = (n^6 - 27*n^4 + 80*n^3 + 158*n^2 - 1028*n + 1200 + (1 - (-1)^n)/2*(8*n^3 - 9*n^2 - 44*n + 45))/48 for n >= 4.

%F G.f.: -25 - 8*x + 3*x^3 + (25 - 67*x - 48*x^2 + 270*x^3 - 41*x^4 - 318*x^5 + 291*x^6 + 354*x^7 - 188*x^8 - 87*x^9 + 49*x^10) / ((1-x)^7*(1+x)^4). - _Vaclav Kotesovec_, Jun 19 2014

%t Drop[CoefficientList[Series[-25 - 8*x + 3*x^3 + (25 - 67*x - 48*x^2 + 270*x^3 - 41*x^4 - 318*x^5 + 291*x^6 + 354*x^7 - 188*x^8 - 87*x^9 + 49*x^10) / ((1-x)^7*(1+x)^4), {x, 0, 20}], x],2] (* _Vaclav Kotesovec_, Jun 19 2014 *)

%Y Cf. A243716, A172134, A243717, A243719, A243720.

%K nonn,easy

%O 2,2

%A _Heinrich Ludwig_, Jun 19 2014