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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
4, 2, 16, 44, 256, 768, 5184, 25344, 186624, 996480, 8294400, 57888000, 530841600, 4006195200, 40642560000, 367408742400, 4064256000000, 39358255104000, 474054819840000, 5254107586560000, 68263894056960000, 804207665479680000, 11242684107325440000 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 2..200

R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976). [E_n, n >= 2.]

MAPLE

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;

MATHEMATICA

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 *)

CROSSREFS

Cf. A005635, A182333.

Sequence in context: A264195 A182872 A137393 * A189741 A303142 A285595

Adjacent sequences:  A122746 A122747 A122748 * A122750 A122751 A122752

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Sep 25 2006

EXTENSIONS

New name from Vaclav Kotesovec, Apr 26 2012

STATUS

approved

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Last modified August 25 15:34 EDT 2019. Contains 326324 sequences. (Running on oeis4.)