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 A099152 Number of n X n permutation matrices in which the sums of the entries of each NorthEast-SouthWest diagonal are 0 or 1. 19
 1, 1, 1, 3, 7, 23, 83, 405, 2113, 12657, 82297, 596483, 4698655, 40071743, 367854835, 3622508685, 38027715185, 424060091065, 5006620130753, 62395131973755, 818456924866815, 11271715349614463 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Numbers of solutions to a modified version of the n-queens problem, in which two queens do not attack each other if they are in the same NorthWest-SouthEast diagonal. Number of perfect extremal Skolem-type sequences of order n. From Emeric Deutsch, Nov 28 2008: (Start) a(n) is also the number of permutations p of {1,2,...,n} for which the numbers p(i)-i (i=1,2,...,n) are distinct. Example: a(4)=7 because we have 4132, 3142, 2413, 4213, 2431, 3241 and 4321. a(n) is also the number of permutations p of {1,2,...,n} for which the numbers p(i)+i (i=1,2,...,n) are distinct. Example: a(4)=7 because we have 1423, 2413, 3142, 1342, 3124, 2314 and 1234. a(n) = A125182(n,n). (End) Also number of transversals in the n X n matrix M defined by M_{ij} = i+j. [Cavenagh-Wanless] REFERENCES D. E. Knuth, The Art of Computer Programming, Volume 4, Pre-fascicle 5B, Introduction to Backtracking, 7.2.2. Backtrack programming. 2018. LINKS N. J. Cavenagh and I. M. Wanless, On the number of transversals in Cayley tables of cyclic groups, Disc. Appl. Math. 158 (2010), 136-146. V. Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 672, 732-736. G. Nordh, Perfect Skolem sequences, arXiv:math/0506155 [math.CO], 2005. Kevin Pratt, Closed-Form Expressions for the n-Queens Problem and Related Problems, arXiv:1609.09585 [cs.DM], 2016. W. Schubert, N-Queens page MATHEMATICA b[i_, p_, s_] := b[i, p, s] = If[p == {}, x^Length[s], Sum[b[i+1, p ~Complement~ {t}, s ~Union~ {t+i}], {t, p}]]; a[n_] := Coefficient[b[1, Range[n], {}], x, n]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 12}] (* Jean-François Alcover, Aug 07 2018, after Alois P. Heinz *) CROSSREFS Cf. A125182. [From Emeric Deutsch, Nov 28 2008] Sequence in context: A346771 A136508 A184935 * A289317 A113860 A080355 Adjacent sequences:  A099149 A099150 A099151 * A099153 A099154 A099155 KEYWORD nonn,nice,more AUTHOR Cecilia Bebeacua and Simone Severini, Nov 16 2004 EXTENSIONS More terms from Ivica Kolar, Nov 23 2004 a(14)-a(18) from Ian Wanless, Jul 30 2010, from the Cavenagh-Wanless paper. a(19),a(20) from W. Schubert, May 27 2011 a(21) from W. Schubert, Feb 26 2012 a(0) = 1 prepended by Joerg Arndt, Sep 16 2018 STATUS approved

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Last modified October 2 15:42 EDT 2022. Contains 357226 sequences. (Running on oeis4.)