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

1,2

Comments

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

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

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

Example

For n=3, there are two trapezoids.

Crossrefs

Strictly less than A006074 for n > 2.

Sequence in context: A155114 A038572 A334667 * A341516 A060992 A064455

Adjacent sequences: A245673 A245674 A245675 * A245677 A245678 A245679

Keyword

nonn

Author

Eli Fox-Epstein, Jul 29 2014

Extensions

Definition clarified by Douglas J. Durian, Sep 24 2017

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

Status

approved