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 A068599 #62 Feb 16 2025 08:32:45 %S A068599 11,20,61,151,332,673,1472,2850,5960,11866,24459,49794,103082 %N A068599 Number of n-uniform tilings. %C A068599 Sequence gives the number of edge-to-edge regular-polygon tilings having n vertex classes relative to the symmetry of the tiling. Allows tilings with two or more vertex classes having the same arrangement of surrounding polygons (vertex type), as long as those classes are distinct within the symmetry of the tiling . %C A068599 There are eleven 1-uniform tilings (also called the "Archimedean" tessellations) which comprise the three regular tessellations (all triangles, squares, or hexagons) plus the eight semiregular tessellations. %D A068599 Marek Čtrnáct, Postings to Tiling Mailing List, 2021 (a(13) announced in posting on Dec 21 2021). %D A068599 B. Grünbaum and G. C. Shephard, Tilings and Patterns, an Introduction, Freeman, 1989; Exercise *6 on p. 70. See Sections 2.1 and 2.2. %H A068599 D. P. Chavey, <a href="https://web.archive.org/web/20100602000932/https://www.beloit.edu/computerscience/faculty/chavey/thesis/">Periodic tilings and tilings by regular polygons</a>, PhD thesis, Univ of Wisconsin, Madison, 1984 (gives a(3)). %H A068599 Marek Čtrnáct and Eryk Kopczyński, <a href="https://zenorogue.github.io/tes-catalog/?c=k-uniform%2F">Tesselation catalog</a> %H A068599 Steven Dutch, <a href="https://stevedutch.net/Symmetry/Uniftil.htm">Uniform Tilings</a> %H A068599 Brian Galebach, <a href="http://ProbabilitySports.com/tilings.html">n-Uniform Tilings</a> %H A068599 Brian Galebach, <a href="/A068599/a068599.tiff">7-Uniform Tiling Example</a>, shows a tiling with 7 vertex classes (7-uniform), and 6 vertex types (6-Archimedean). %H A068599 El Jj, <a href="https://youtu.be/N5DGzm7xHRA?si=DY9kAN6NcSOiNwaq">Deux (deux ?) minutes pour... classer les pavages !</a>, youtube video (in French). %H A068599 Joris Kattemölle, <a href="https://arxiv.org/abs/2402.08752">Edge coloring lattice graphs</a>, arXiv:2402.08752 [quant-ph], 2024. %H A068599 Ng Lay Ling, <a href="https://citeseerx.ist.psu.edu/pdf/19e8b6984d0deba7eb4345d5624e17be32f7e3de">Honours Project - Tilings and Patterns</a>. %H A068599 N. J. A. Sloane, Coordination Sequences, Planing Numbers, and Other Recent Sequences (II), Experimental Mathematics Seminar, Rutgers University, Jan 31 2019, <a href="https://vimeo.com/314786942">Part I</a>, <a href="https://vimeo.com/314790822">Part 2</a>, <a href="https://oeis.org/A320487/a320487.pdf">Slides.</a> (Mentions this sequence) %H A068599 Hui Wang, Mengman Liu, Chuhua Ding, and Yi Ding, <a href="https://doi.org/10.1016/j.foar.2024.08.002">A systematic method of generating hinged tessellations by adding hinged plates based on dual graphs</a>, Frontiers Archit. Res. (2024). See Table 1. %H A068599 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UniformTessellation.html">Uniform Tessellation</a> %Y A068599 Cf. A068600. %K A068599 hard,nice,more,nonn %O A068599 1,1 %A A068599 _Brian Galebach_, Mar 28 2002 %E A068599 151 and 332 found by _Brian Galebach_ on Apr 30 2002, 673 on Aug 06 2003, 1472 on Apr 28 2020 %E A068599 a(8)-a(13) found by Marek Čtrnáct in 2021. - _N. J. A. Sloane_, Dec 21 2021