A245676 Number of convex polyaboloes (or convex polytans): number of distinct convex shapes that can be formed with n congruent isosceles right triangles. Reflections are not counted as different.
1, 3, 2, 6, 3, 7, 5, 11, 5, 10, 7, 14, 7, 16, 11, 20, 9, 17, 13, 22, 12, 25, 18, 27, 14, 24, 20, 31, 18, 36, 26, 37, 19, 34, 28, 38, 24, 45, 34, 47, 26, 41, 36, 49, 35, 61, 44, 54, 32, 54, 45, 56, 40, 71, 56, 63, 40, 66, 56, 72, 49, 86, 66, 76, 51, 74, 67, 77
Offset: 1
Keywords
Examples
For n=3, there are two trapezoids.
Links
- Douglas J. Durian, Table of n, a(n) for n = 1..750
- Douglas J. Durian, Illustration of shapes for n=1..20.
- Eli Fox-Epstein, Ryuhei Uehara, The Convex Configurations of "Sei Shonagon Chie no Ita" and Other Dissection Puzzles, arXiv:1407.1923 [cs.CG], (8-July-2014)
- Eli Fox-Epstein, Kazuho Katsumata, Ryuhei Uehara, The Convex Configurations of “Sei Shonagon Chie no Ita,” Tangram, and Other Silhouette Puzzles with Seven Pieces, Institute of Electronics, Information Communication Engineers - Transactions on Fundamentals, E99-A (2016), 1084-1089.
- Paul Scott, Convex Tangrams, Australian Mathematics Teacher, 62 (2006), 2-5. Confirms a(16)=20.
- Fu Traing Wang and Chuan-Chih Hsiung, A Theorem on the Tangram, American Mathematical Monthly, 49 (1942), 596-599. Proves a(16)=20 and that convex polyabolos have no more than eight sides.
- Douglas J. Durian, Description of shapes for n = 1..750
Crossrefs
Strictly less than A006074 for n > 2.
Formula
Extensions
Definition clarified by Douglas J. Durian, Sep 24 2017
a(51) and beyond from Douglas J. Durian, Jan 24 2020
Comments