This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A002562 M0180 N0068 #78 Feb 16 2025 08:32:26 %S A002562 1,0,0,1,2,1,6,12,46,92,341,1787,9233,45752,285053,1846955,11977939, %T A002562 83263591,621012754,4878666808,39333324973,336376244042,3029242658210, %U A002562 28439272956934,275986683743434,2789712466510289,29363495934315694 %N A002562 Number of ways of placing n nonattacking queens on n X n board (symmetric solutions count only once). %D A002562 Martin Gardner, Fractal Music, Hypercards and More, Freeman, NY, 1991, p. 231-233. %D A002562 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). %D A002562 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %D A002562 M. B. Wells, Elements of Combinatorial Computing. Pergamon, Oxford, 1971, p. 238. %H A002562 J. R. Bitner and E. M. Reingold, <a href="/A002562/a002562.pdf">Backtrack programming techniques</a>, Commun. ACM, 18 (1975), 651-656. [Annotated scanned copy] %H A002562 J. R. Bitner and E. M. Reingold, <a href="http://dx.doi.org/10.1145/361219.361224">Backtrack programming techniques</a>, Commun. ACM, 18 (1975), 651-656. %H A002562 P. Capstick and K. McCann, <a href="/A000170/a000170_1.pdf">The problem of the n queens</a>, apparently unpublished, no date (circa 1990?) [Scanned copy] %H A002562 V. Chvatal, <a href="http://users.encs.concordia.ca/~chvatal/8queens.html">All solutions to the problem of eight queens</a> %H A002562 V. Chvatal, <a href="/A002562/a002562_1.pdf">All solutions to the problem of eight queens</a> [Cached copy, pdf format, with permission] %H A002562 Popular Computing (Calabasas, CA), <a href="/A002562/a002562.png">8 Queens</a>, Vol. 2, No. 13, Apr 1974, page PC13-1. Illustrates a(8)=12. %H A002562 Popular Computing (Calabasas, CA), <a href="/A002562/a002562_1.png">8 Queens</a>, Vol. 2, No. 13, Apr 1974, page PC13-2. %H A002562 Popular Computing (Calabasas, CA), <a href="/A002562/a002562_2.png">8 Queens</a>, Vol. 2, No. 13, Apr 1974, page PC13-3. %H A002562 Popular Computing (Calabasas, CA), <a href="/A002562/a002562_3.png">8 Queens</a>, Vol. 2, No. 13, Apr 1974, page PC13-4. %H A002562 Thomas Preusser, <a href="https://web.archive.org/web/20171110040233/http://queens.inf.tu-dresden.de/">Queens%40TUD</a>-Project %H A002562 E. M. Reingold, <a href="/A000170/a000170_2.pdf">Letter to N. J. A. Sloane</a>, Dec 27 1973 %H A002562 M. A. Sainte-Laguë, <a href="https://eudml.org/doc/192551">Les Réseaux (ou Graphes)</a>, Mémorial des Sciences Mathématiques, Fasc. 18, Gauthier-Villars, Paris, 1923, 64 pages. See p. 47. %H A002562 M. A. Sainte-Laguë, <a href="/A002560/a002560.pdf">Les Réseaux (ou Graphes)</a>, Mémorial des Sciences Mathématiques, Fasc. 18, Gauthier-Villars, Paris, 1923, 64 pages. See p. 47. [Incomplete annotated scan of title page and pages 18-51] %H A002562 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/QueensProblem.html">Queens Problem.</a> %H A002562 M. B. Wells, <a href="/A000170/a000170.pdf">Elements of Combinatorial Computing</a>, Pergamon, Oxford, 1971. [Annotated scanned copy of pages 237-240] %H A002562 Wikipedia, <a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle">Eight queens puzzle</a>. %F A002562 a(n) = (1/8) * (Q(n) + P(n) + 2 * R(n)), where Q(n) = A000170(n) [all solutions], P(n) = A032522(n) [point symmetric solutions] and R(n) = A033148(n) [rotationally symmetric solutions]. %e A002562 a(4) = 1: %e A002562 +---------+ %e A002562 | . . Q . | %e A002562 | Q . . . | %e A002562 | . . . Q | %e A002562 | . Q . . | %e A002562 +---------+ %e A002562 a(5) = 2: %e A002562 +-----------+ +-----------+ %e A002562 | . . . Q . | | . . . Q . | %e A002562 | . Q . . . | | Q . . . . | %e A002562 | . . . . Q | | . . Q . . | %e A002562 | . . Q . . | | . . . . Q | %e A002562 | Q . . . . | | . Q . . . | %e A002562 +-----------+ +-----------+ %e A002562 a(6) = 1: %e A002562 +-------------+ %e A002562 | . . . . Q . | %e A002562 | . . Q . . . | %e A002562 | Q . . . . . | %e A002562 | . . . . . Q | %e A002562 | . . . Q . . | %e A002562 | . Q . . . . | - _Hugo Pfoertner_, Mar 17 2019 %e A002562 +-------------+ %e A002562 a(7) = 6: %e A002562 +---------------+ +---------------+ +---------------+ %e A002562 | Q . . . . . . | | Q . . . . . . | | . Q . . . . . | %e A002562 | . . Q . . . . | | . . . Q . . . | | . . . Q . . . | %e A002562 | . . . . Q . . | | . . . . . . Q | | Q . . . . . . | %e A002562 | . . . . . . Q | | . . Q . . . . | | . . . . . . Q | %e A002562 | . Q . . . . . | | . . . . . Q . | | . . . . Q . . | %e A002562 | . . . Q . . . | | . Q . . . . . | | . . Q . . . . | %e A002562 | . . . . . Q . | | . . . . Q . . | | . . . . . Q . | %e A002562 +---------------+ +---------------+ +---------------+ %e A002562 . %e A002562 +---------------+ +---------------+ +---------------+ %e A002562 | . Q . . . . . | | . Q . . . . . | | . Q . . . . . | %e A002562 | . . . . Q . . | | . . . . Q . . | | . . . . . Q . | %e A002562 | Q . . . . . . | | . . . . . . Q | | . . Q . . . . | %e A002562 | . . . Q . . . | | . . . Q . . . | | . . . . . . Q | %e A002562 | . . . . . . Q | | Q . . . . . . | | . . . Q . . . | %e A002562 | . . Q . . . . | | . . Q . . . . | | Q . . . . . . | %e A002562 | . . . . . Q . | | . . . . . Q . | | . . . . Q . . | %e A002562 +---------------+ +---------------+ +---------------+ %e A002562 - _Hugo Pfoertner_, Mar 18 2019 %Y A002562 Cf. A000170, A032522, A033148. %K A002562 nonn,nice %O A002562 1,5 %A A002562 _N. J. A. Sloane_ %E A002562 a(17) and a(18) found by Ulrich Schimke in Goettingen, Germany (UlrSchimke(AT)aol.com) %E A002562 Formula and a(19) to a(23) added by _Matthias Engelhardt_ in Nuremberg, Germany, Jan 23 2000 %E A002562 Terms (calculated from formula) added by _Thomas B. Preußer_, Dec 15 2008 %E A002562 a(26) (derived from formula after recent extension of A000170) added by _Thomas B. Preußer_, Jul 12 2009 %E A002562 a(27) (derived from formula after recent extension of A000170) added by _Thomas B. Preußer_, Sep 23 2016