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 A293061 #10 Oct 07 2017 22:09:49
%S A293061 1,2,2,10,7,17,32,75,80,230,271,343,1091,1594,4894,955
%N A293061 Triangle read by rows (n >= 0, 0 <= k <= n): T(n,k) = number of k-dimensional subperiodic groups in n-dimensional space, counting enantiomorphs.
%C A293061 T(n,0) count n-dimensional crystallographic point groups, T(n,n) count n-dimensional space groups (i.e., right border is A006227). The name "subperiodic groups" is usually related to the case 0 < k < n only, i.e., symmetry groups of n-dimensional objects including k independent translations which are subgroups of some n-dimensional space groups.
%C A293061 The Bohm symbols for these groups are G_{n,k}, except for the case k=n, when it is G_n.
%C A293061 Some groups have their own names:
%C A293061 T(2,1): frieze groups
%C A293061 T(2,2): wallpaper groups
%C A293061 T(3,1): rod groups
%C A293061 T(3,2): layer groups
%C A293061 [Palistrant, 2012, p. 476] gives correct T(4,k), k=0,1,2,3 but incorrect T(4,4). For correct value of T(4,4), see [Souvignier, 2006, p. 80].
%H A293061 M. I. Aroyo et al, <a href="http://www.cryst.ehu.es/">Bilbao Crystallographic Server</a>
%H A293061 International Union of Crystallography, <a href="http://it.iucr.org/">International Tables for Crystallography</a>, volumes A and E.
%H A293061 A. F. Palistrant, <a href="https://doi.org/10.1134/S1063774512040104">Complete scheme of four-dimensional crystallographic symmetry groups</a>, Crystallography Reports, 57 (2012), 471-477.
%H A293061 W. Plesken and T. Schulz, <a href="http://wwwb.math.rwth-aachen.de/carat/">CARAT Homepage</a>
%H A293061 W. Plesken and T. Schulz, <a href="/A006226/a006226.pdf">CARAT Homepage</a> [Cached copy in pdf format (without subsidiary pages), with permission]
%H A293061 B. Souvignier, <a href="https://doi.org/10.1524/zkri.2006.221.1.77">The four-dimensional magnetic point and space groups</a>, Z. Kristallogr., 221 (2006), 77-82.
%H A293061 Wikipedia: <a href="https://en.wikipedia.org/wiki/Space_group">Space group</a>, <a href="https://en.wikipedia.org/wiki/Crystallographic_point_group">Crystallographic point group</a>, <a href="https://en.wikipedia.org/wiki/Line_group">Line group</a>, <a href="https://en.wikipedia.org/wiki/Frieze_group">Frieze group</a>, <a href="https://en.wikipedia.org/wiki/Wallpaper_group">Wallpaper group</a>, <a href="https://en.wikipedia.org/wiki/Rod_group">Rod group</a>, <a href="https://en.wikipedia.org/wiki/Layer_group">Layer group</a>
%H A293061 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%e A293061 The triangle begins:
%e A293061 1;
%e A293061 2, 2;
%e A293061 10, 7, 17;
%e A293061 32, 75, 80, 230;
%e A293061 271, 343, 1091, 1594, 4894;
%e A293061 955, ...
%Y A293061 Cf. A006227, A293060, A293062, A293063.
%K A293061 nonn,tabl,hard,more
%O A293061 0,2
%A A293061 _Andrey Zabolotskiy_, Sep 29 2017