This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A007631 Number of solutions to non-attacking reflecting queens problem. (Formerly M0929) 2
 1, 1, 0, 0, 2, 4, 0, 2, 10, 32, 38, 140, 496, 1186, 3178, 16792, 82038, 289566, 1139874, 5914118, 33800010, 142337180, 721286448, 4384569864 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS a(n) is the number of ways to pair the natural numbers from 1 to n with those between n+1 and 2*n into n pairs (xi,yi) such that the 2*n numbers yi+i and yi-i are all different. - Michel Marcus,  Apr 27 2016 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Jordan Bell, Brett Stevens, A survey of known results and research areas for n-queens, Discrete Mathematics, Volume 309 (2009), pp 1-31. M. Gardner, Fractal Music, Hypercards and More, Freeman, NY, 1991, p. 240. G. B. Huff, On pairings of the first 2n natural numbers, Acta. Arith. 23 (1973) 117-126. D. A. Klarner, The Problem of Reflecting Queens, The American Mathematical Monthly, Vol. 74, No. 8 (Oct., 1967), pp. 953-955. M. Slater, Number theory Research Problem 1, Bull. Amer. Math. Soc. 69 (1963), 333. EXAMPLE For n = 4, ((1,7), (2,5), (3,8), (4,6)) is an instance of such grouping. ((2,5), (1,7), (3,8), (4,6)) is considered to be the same grouping. PROG (PARI) a(n) = {nb = 0; for (j=0, n!-1, vp = numtoperm(n, j); vb = vector(n, k, vp[k]+n); vs = vector(n, k, vb[k]+k); vd = vector(n, k, vb[k]-k); if (#vs + #vd == #Set(concat(vs, vd)), nb++); ); nb; } \\ Michel Marcus,  Apr 27 2016 CROSSREFS Cf. A000170, A002968, A051223, A051224, A272363. Sequence in context: A256280 A153182 A111818 * A281765 A155517 A123514 Adjacent sequences:  A007628 A007629 A007630 * A007632 A007633 A007634 KEYWORD nonn,nice,more,changed AUTHOR EXTENSIONS a(18)-a(21) from Sean A. Irvine, Jan 13 2018 a(0)-a(3) prepended by Michel Marcus, Oct 03 2018 a(22) from Sean A. Irvine, Oct 04 2018 a(23) from Sean A. Irvine, Oct 07 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 16 20:34 EDT 2018. Contains 316275 sequences. (Running on oeis4.)