A307293 Number of color plane groups of index n.

17, 46, 23, 96, 14, 90, 15, 166, 40, 75, 13, 219, 16, 80, 34, 262, 14, 174, 15, 205, 38, 88, 13, 433, 31, 103, 48, 222, 14, 213, 15, 395, 36, 111, 24, 452, 16, 116, 40, 416, 14, 250, 15, 265, 62, 124, 13, 741, 32, 193, 38, 300, 14, 303, 24, 468, 42, 147, 13, 627, 16

Offset

1,1

References

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

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

Links

Table of n, a(n) for n=1..61.

R. L. E. Schwarzenberger, Colour symmetry: Part two, Bulletin of the London Mathematical Society 16.3 (1984): 216-229. See page 221.

R. L. E. Schwarzenberger, Review of "The Mathematical Theory of Chromatic Plane Ornaments" by Thomas W. Wieting, Bull. London Math. Soc., 15 (1983), 163-164.

Marjorie Senechal, Color groups, Discrete Applied Mathematics, 1 (1979), 51-73.

Formula

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

Example

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

Crossrefs

Cf. A004029, A307292.

Sequence in context: A221752 A032698 A120099 * A045570 A058205 A329951

Adjacent sequences: A307290 A307291 A307292 * A307294 A307295 A307296

Keyword

nonn

Author

N. J. A. Sloane, Apr 08 2019

Extensions

a(1) and a(16)-a(60) from Wieting added by Andrey Zabolotskiy, Apr 09 2019

a(61) added by Andrey Zabolotskiy, May 18 2022

Status

approved