A177756 - OEIS

%I #17 Aug 31 2024 19:25:15

%S 0,0,6,128,600,2688,7350,19968,42336,89600,163350,297600,490776,

%T 809088,1242150,1906688,2774400,4036608,5633766,7862400,10613400,

%U 14326400,18818646,24718848,31740000

%N Number of ways to place 3 nonattacking bishops on an n X n toroidal board.

%H Vincenzo Librandi, <a href="/A177756/b177756.txt">Table of n, a(n) for n = 1..1000</a>

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (2, 4, -10, -5, 20, 0, -20, 5, 10, -4, -2, 1).

%F Explicit formula: 1/12*(n-2)^2*n^2*(2*n^2-4*n+5+3(-1)^n).

%F G.f.: -2*x^3*(3*x^8+58*x^7+160*x^6+518*x^5+442*x^4+518*x^3+160*x^2+58*x+3)/((x-1)^7*(x+1)^5).

%t CoefficientList[Series[- 2 x^2 * (3 x^8 + 58 x^7 + 160 x^6 + 518 x^5 + 442 x^4 + 518 x^3 + 160 x^2 + 58 x + 3)/((x - 1)^7 * (x + 1) ^5), {x, 0,1 50}], x] (* _Vincenzo Librandi_, May 31 2013 *)

%t LinearRecurrence[{2,4,-10,-5,20,0,-20,5,10,-4,-2,1},{0,0,6,128,600,2688,7350,19968,42336,89600,163350,297600},30] (* _Harvey P. Dale_, Aug 31 2024 *)

%Y Cf. A172124, A177755.

%K nonn,easy

%O 1,3

%A _Vaclav Kotesovec_, May 13 2010