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 A146304 Number of distinct ways to place bishops (up to 2n-2) on an n*n chessboard so that no bishop is attacking another and that it is not possible to add another bishop. 8
 1, 4, 10, 64, 660, 7744, 111888, 1960000, 40829184, 989479936, 27559645440, 870414361600, 30942459270912, 1225022400102400, 53716785891102720, 2589137004664520704, 136573353235553058816, 7838079929528363843584, 487668908919708442951680, 32741107405951528945844224 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Number of maximal independent vertex sets (and minimal vertex covers) in the n X n bishop graph. - Eric W. Weisstein, Jun 04 2017 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 Andrew Howroyd, Algorithm and explanation of PARI code Eric Weisstein's World of Mathematics, Bishop Graph Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set Eric Weisstein's World of Mathematics, Minimal Vertex Cover FORMULA Conjectured to be a(n) = O(n^(n-1)). a(n) = A290594(n) * A290613(n) for n > 1. - Andrew Howroyd, Aug 09 2017 EXAMPLE For n=2, the a(n) = 4 solutions are to place two bishops on the same row (two solutions) or column (two solutions). MATHEMATICA M[sig_List, n_, k_, d_, x_] := M[sig, n, k, d, x] = If[n == 0, Boole[k == 0], If[k > 0, k*x*M[sig, n - 1, k - 1, d, x], 0] + If[k < n && sig[[n]] > d, (sig[[n]] - d)*x*M[sig, n - 1, k, d + 1, x], 0] + If[k + sig[[n]] - d < n, M[sig, n - 1, k + sig[[n]] - d, sig[[n]], x], 0]]; Q[sig_List, x_] := M[sig, Length[sig], 0, 0, x]; Bishop[n_, white_] := Table[n - i + If[white == 1, 1 - Mod[i, 2], Mod[i, 2]], {i, 1, n - If[white == 1, Mod[n, 2], 1 - Mod[n, 2]]}] a[n_] := Q[Bishop[n, 0], 1]*Q[Bishop[n, 1], 1]; Table[a[n], {n, 1, 20}] (* Jean-François Alcover, Jun 15 2017, translated from Andrew Howroyd's PARI code *) PROG (PARI) \\ Needs memoization - see note on algorithm for a faster version. M(sig, n, k, d, x)={if(n==0, k==0, if(k>0, k*x*M(sig, n-1, k-1, d, x), 0) + if(kd, (sig[n]-d)*x*M(sig, n-1, k, d+1, x), 0) + if(k+sig[n]-d

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Last modified November 12 04:21 EST 2019. Contains 329051 sequences. (Running on oeis4.)