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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.
8
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
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.
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
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