A177755 Number of ways to place 2 nonattacking bishops on an n X n toroidal board.

0, 4, 18, 80, 200, 468, 882, 1600, 2592, 4100, 6050, 8784, 12168, 16660, 22050, 28928, 36992, 46980, 58482, 72400, 88200, 106964, 128018, 152640, 180000

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

V. Kotesovec, Non-attacking chess pieces, 6ed, 2013

Index entries for linear recurrences with constant coefficients, signature (2, 2, -6, 0, 6, -2, -2, 1).

Formula

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

G.f.: -2*x^2*(x^5+8*x^4+14*x^3+18*x^2+5*x+2)/((x-1)^5*(x+1)^3).

a(1)=0, a(2)=4, a(3)=18, a(4)=80, a(5)=200, a(6)=468, a(7)=882, a(8)=1600, a(n)=2*a(n-1)+2*a(n-2)-6*a(n-3)+6*a(n-5)-2*a(n-6)-2*a(n-7)+a(n-8). - Harvey P. Dale, Mar 06 2013

Mathematica

Table[(n^2 (2n^2-4n+3+(-1)^n))/4, {n, 30}] (* or *) LinearRecurrence[ {2, 2, -6, 0, 6, -2, -2, 1}, {0, 4, 18, 80, 200, 468, 882, 1600}, 30] (* Harvey P. Dale, Mar 06 2013 *)
CoefficientList[Series[- 2 x (x^5 + 8 x^4 + 14 x^3 + 18 x^2 + 5 x + 2) / ((x - 1)^5 (x + 1)^3), {x, 0, 50}], x] (* Vincenzo Librandi, May 31 2013 *)

Crossrefs

Cf. A172123.

Sequence in context: A208309 A112619 A196810 * A037965 A045902 A090017

Adjacent sequences: A177752 A177753 A177754 * A177756 A177757 A177758

Keyword

nonn,easy

Author

Vaclav Kotesovec, May 13 2010

Status

approved