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 A006052 M5482 #130 Jul 21 2025 13:24:35 %S A006052 1,0,1,880,275305224,17753889197660635632 %N A006052 Number of magic squares of order n composed of the numbers from 1 to n^2, counted up to rotations and reflections. %C A006052 a(4) computed by Frenicle de Bessy (1605? - 1675), published in 1693. The article mentions the 880 squares and considers also 5*5, 6*6, 8*8, and other squares. - _Paul Curtz_, Jul 13 and Aug 12 2011 %C A006052 a(5) computed by Richard C. Schroeppel in 1973. %C A006052 According to Pinn and Wieczerkowski, a(6) = (0.17745 +- 0.00016) * 10^20. - _R. K. Guy_, May 01 2004 %C A006052 a(6) computed by Hidetoshi Mino in 2024 - _Hidetoshi Mino_, May 31 2024 %D A006052 E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Vol. II, pp. 778-783 gives the 880 4 X 4 squares. %D A006052 M. Gardner, Mathematical Games, Sci. Amer. Vol. 249 (No. 1, 1976), p. 118. %D A006052 M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 216. %D A006052 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A006052 Ian Cameron, Adam Rogers and Peter Loly, <a href="https://web.archive.org/web/20150911053529/http://www.physics.umanitoba.ca/~icamern/Poland2012/Data/Bewedlo%20Codex.pdf">"The Library of Magical Squares" -- a summary of the main results for the Shannon entropy of magic and Latin squares: isentropic clans and indexing, in celebration of George Styan's 75th</a>. %H A006052 Bernard Frénicle de Bessy, <a href="http://babel.hathitrust.org/cgi/pt?u=1&num=423&seq=11&view=image&size=100&id=ucm.5323750390">Des carrez ou tables magiques</a>, Divers ouvrages de mathématique et de physique (1693), pp. 423-483. %H A006052 Bernard Frénicle de Bessy, <a href="http://babel.hathitrust.org/cgi/pt?u=1&num=484&seq=9&view=image&size=100&id=ucm.5323750390">Table générale des carrez de quatre</a>, Divers ouvrages de mathématique et de physique (1693), pp. 484-503. %H A006052 Skylar R. Croy, Jeremy A. Hansen, and Daniel J. McQuillan, <a href="https://doi.org/10.1609/socs.v7i1.18408">Calculating the Number of Order-6 Magic Squares with Modular Lifting</a>, Proceedings of the Ninth International Symposium on Combinatorial Search (SoCS 2016). %H A006052 Mahadi Hasan and Md. Masbaul Alam Polash, <a href="https://doi.org/10.1007/978-981-13-8942-9_7">An Efficient Constraint-Based Local Search for Maximizing Water Retention on Magic Squares</a>, Emerging Trends in Electrical, Communications, and Information Technologies, Lecture Notes in Electrical Engineering book series (LNEE 2019) Vol. 569, 71-79. %H A006052 Hidetoshi Mino, <a href="https://magicsquare6.net/">The number of magic squares of order 6</a>. %H A006052 Hidetoshi Mino, <a href="https://www.youtube.com/watch?v=PqksUOAwr58">Fast enumeration of magic squares</a>, YouTube video, 2025. %H A006052 I. Peterson, <a href="https://web.archive.org/web/20080421150630/http://www.sciencenews.org/pages/sn_arc99/10_16_99/mathland.htm">Magic Tesseracts</a>. %H A006052 K. Pinn and C. Wieczerkowski, <a href="https://arxiv.org/abs/cond-mat/9804109">Number of magic squares from parallel tempering Monte Carlo</a>, arXiv:cond-mat/9804109 [cond-mat.stat-mech], 1998; Internat. J. Modern Phys., 9 (4) (1998) 541-546. %H A006052 Tyler Pringle, <a href="https://cklixx.people.wm.edu/teaching/math400/Tyler.pdf">Magic Squares and Using Magic Series for Theory</a>, The College of William and Mary (2024). See pp. 6, 9. %H A006052 Artem Ripatti, <a href="https://arxiv.org/abs/1807.02983">On the number of semi-magic squares of order 6</a>, arXiv:1807.02983 [math.CO], 2018. See Table 1 p. 2. %H A006052 R. Schroeppel, <a href="/A006052/a006052_2.pdf">Emails to N. J. A. Sloane, Jun. 1991</a>. %H A006052 N. J. A. Sloane & J. R. Hendricks, <a href="/A006052/a006052_3.pdf">Correspondence, 1974</a>. %H A006052 Walter Trump, <a href="http://www.trump.de/magic-squares/howmany.html">How many magic squares are there? - Results of historical and computer enumeration</a>. %H A006052 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MagicSquare.html">Magic Square</a>. %H A006052 <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a> %e A006052 An illustration of the unique (up to rotations and reflections) magic square of order 3: %e A006052 +---+---+---+ %e A006052 | 2 | 7 | 6 | %e A006052 +---+---+---+ %e A006052 | 9 | 5 | 1 | %e A006052 +---+---+---+ %e A006052 | 4 | 3 | 8 | %e A006052 +---+---+---+ %Y A006052 Cf. A270876, A271103, A271104. %K A006052 nonn,hard,nice,more %O A006052 1,4 %A A006052 _N. J. A. Sloane_ %E A006052 Definition corrected by _Max Alekseyev_, Dec 25 2015 %E A006052 a(6) from _Hidetoshi Mino_, Jul 17 2023 %E A006052 Incorrect a(6) removed by _Hidetoshi Mino_, Sep 07 2023 %E A006052 a(6) from _Hidetoshi Mino_, May 31 2024