A307293 - OEIS

%I #17 May 19 2022 09:20:58

%S 17,46,23,96,14,90,15,166,40,75,13,219,16,80,34,262,14,174,15,205,38,

%T 88,13,433,31,103,48,222,14,213,15,395,36,111,24,452,16,116,40,416,14,

%U 250,15,265,62,124,13,741,32,193,38,300,14,303,24,468,42,147,13,627,16

%N Number of color plane groups of index n.

%D Branko Grünbaum and G. C. Shephard, Tilings and Patterns, W. H. Freeman, New York, 1987, chapter 8 "Colored patterns and tilings".

%D Thomas W. Wieting, The Mathematical Theory of Chromatic Plane Ornaments, Marcel Dekker, Inc., 1982. See Table 11 at pages 250-254.

%H R. L. E. Schwarzenberger, <a href="https://doi.org/10.1112/blms/16.3.216">Colour symmetry: Part two</a>, Bulletin of the London Mathematical Society 16.3 (1984): 216-229. See page 221.

%H R. L. E. Schwarzenberger, <a href="https://doi.org/10.1112/blms/15.2.163">Review of "The Mathematical Theory of Chromatic Plane Ornaments" by Thomas W. Wieting</a>, Bull. London Math. Soc., 15 (1983), 163-164.

%H Marjorie Senechal, <a href="https://doi.org/10.1016/0166-218X(79)90014-3">Color groups</a>, Discrete Applied Mathematics, 1 (1979), 51-73.

%F a(p) = 16, 15, 14, 13 if p == 1, 7, 5, 11 (mod 12), respectively, and a(p^2) = a(p) + 17, where p is a prime greater than 3. These formulas are found by Senechal. Schwarzenberger (1983) says that her results are correct for these cases, while some other results have essentially been corrected by Wieting. - _Andrey Zabolotskiy_, May 18 2022

%e a(1) = A004029(2), a(2) = A307292(2).

%Y Cf. A004029, A307292.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Apr 08 2019

%E a(1) and a(16)-a(60) from Wieting added by _Andrey Zabolotskiy_, Apr 09 2019

%E a(61) added by _Andrey Zabolotskiy_, May 18 2022