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A122749 Number of arrangements of n non-attacking bishops on an n X n board such that every square of the board is controlled by at least one bishop. 7

%I

%S 4,2,16,44,256,768,5184,25344,186624,996480,8294400,57888000,

%T 530841600,4006195200,40642560000,367408742400,4064256000000,

%U 39358255104000,474054819840000,5254107586560000,68263894056960000,804207665479680000,11242684107325440000

%N Number of arrangements of n non-attacking bishops on an n X n board such that every square of the board is controlled by at least one bishop.

%H Vincenzo Librandi, <a href="/A122749/b122749.txt">Table of n, a(n) for n = 2..200</a>

%H R. W. Robinson, <a href="http://dx.doi.org/10.1007/BFb0097382">Counting arrangements of bishops</a>, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976). [E_n, n >= 2.]

%p E:=proc(n) local k; if n mod 2 = 0 then k := n/2; if k mod 2 = 0 then RETURN( (k!*(k+2)/2)^2 ); else RETURN( ((k-1)!*(k+1)^2/2)^2 ); fi; else k := (n-1)/2; if k mod 2 = 0 then RETURN( ((k!)^2/12)*(3*k^3+16*k^2+18*k+8) ); else RETURN( ((k-1)!*(k+1)!/12)*(3*k^3+13*k^2-k-3) ); fi; fi; end;

%t Table[If[n==1,1,1/768*(2*(3*n^3+23*n^2+17*n+21)*(((n-1)/2)!)^2*(1-(-1)^n+2*Sin[(Pi*n)/2])-2*(3*n^3+17*n^2-47*n+3)*((n-3)/2)!*((n+1)/2)!*((-1)^n+2*Sin[(Pi*n)/2]-1)+3*(n+2)^4*((n/2-1)!)^2*((-1)^n-2*Cos[(Pi*n)/2]+1)+12*(n+4)^2*((n/2)!)^2*((-1)^n+2*Cos[(Pi*n)/2]+1))],{n,2,25}] (* _Vaclav Kotesovec_, Apr 26 2012 *)

%Y Cf. A005635, A182333.

%K nonn

%O 2,1

%A _N. J. A. Sloane_, Sep 25 2006

%E New name from _Vaclav Kotesovec_, Apr 26 2012

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Last modified October 19 01:25 EDT 2019. Contains 328211 sequences. (Running on oeis4.)