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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 25 20:01 EDT 2021. Contains 347659 sequences. (Running on oeis4.)