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 A177755 Number of ways to place 2 nonattacking bishops on an n X n toroidal board. 8
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified November 27 21:40 EST 2022. Contains 358406 sequences. (Running on oeis4.)