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

Author

Eli Fox-Epstein, Jul 29 2014

Keywords

• nonn

Comments

Side numbers range from 3 to 8. See Wang and Hsiung (1942). - Douglas J. Durian, Sep 24 2017

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

a(n) = A093709(n) + A292146(n) + A292147(n) + A292148(n) + A292149(n) + A292150(n). [Wang and Hsiang (1942)] - Douglas J. Durian, Sep 24 2017

Extensions

Definition clarified by Douglas J. Durian, Sep 24 2017

a(51) and beyond from Douglas J. Durian, Jan 24 2020