cp's OEIS Frontend

A068600 Number of n-uniform tilings having n different arrangements of polygons about their vertices.

%I A068600 #22 Aug 06 2024 09:23:24
%S A068600 11,20,39,33,15,10,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A068600 0,0,0,0,0,0
%N A068600 Number of n-uniform tilings having n different arrangements of polygons about their vertices.
%C A068600 Sequence gives the number of edge-to-edge regular-polygon tilings having n topologically distinct vertex types, with each vertex type having a different arrangement of surrounding polygons. Does not allow for tilings with two or more vertex types having the same arrangement of surrounding polygons, even when those vertices are topologically distinct. There are no 8- or higher-uniform tilings having the equivalent number of distinct polygon arrangements.
%C A068600 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. (See A250120. - _N. J. A. Sloane_, Nov 29 2014)
%D A068600 This sequence was originally calculated by Otto Krotenheerdt.
%D A068600 Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987, page 69.
%D A068600 Krotenheerdt, Otto. "Die homogenen Mosaike n-ter Ordnung in der euklidischen Ebene," Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg. Math.-natur. Reihe, 18(1969), 273-290; 19 (1970)19-38 and 97-122.
%H A068600 Steven Dutch, <a href="https://stevedutch.net/Symmetry/Uniftil.htm">Uniform Tilings</a>
%H A068600 Brian L. Galebach, <a href="http://ProbabilitySports.com/tilings.html">n-Uniform Tilings</a>
%H A068600 Ng Lay Ling, <a href="https://citeseerx.ist.psu.edu/pdf/19e8b6984d0deba7eb4345d5624e17be32f7e3de">Honours Project - Tilings and Patterns</a>.
%Y A068600 Cf. A068599.
%Y A068600 List of coordination sequences for uniform planar nets: A008458 (the planar net 3.3.3.3.3.3), A008486 (6^3), A008574 (4.4.4.4 and 3.4.6.4), A008576 (4.8.8), A008579 (3.6.3.6), A008706 (3.3.3.4.4), A072154 (4.6.12), A219529 (3.3.4.3.4), A250120(3.3.3.3.6), A250122 (3.12.12).
%K A068600 nonn
%O A068600 1,1
%A A068600 _Brian Galebach_, Mar 28 2002