cp's OEIS Frontend

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.

%I A245676 #61 Jan 26 2020 01:14:14
%S A245676 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,
%T A245676 20,31,18,36,26,37,19,34,28,38,24,45,34,47,26,41,36,49,35,61,44,54,32,
%U A245676 54,45,56,40,71,56,63,40,66,56,72,49,86,66,76,51,74,67,77
%N 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.
%C A245676 Side numbers range from 3 to 8. See Wang and Hsiung (1942). - _Douglas J. Durian_, Sep 24 2017
%H A245676 Douglas J. Durian, <a href="/A245676/b245676.txt">Table of n, a(n) for n = 1..750</a>
%H A245676 Douglas J. Durian, <a href="/A245676/a245676.pdf">Illustration of shapes for n=1..20.</a>
%H A245676 Eli Fox-Epstein, Ryuhei Uehara, <a href="http://arxiv.org/abs/1407.1923">The Convex Configurations of "Sei Shonagon Chie no Ita" and Other Dissection Puzzles</a>, arXiv:1407.1923 [cs.CG], (8-July-2014)
%H A245676 Eli Fox-Epstein, Kazuho Katsumata, Ryuhei Uehara, <a href="http://doi.org/10.1587/transfun.E99.A.1084">The Convex Configurations of “Sei Shonagon Chie no Ita,” Tangram, and Other Silhouette Puzzles with Seven Pieces</a>, Institute of Electronics, Information Communication Engineers - Transactions on Fundamentals, E99-A (2016), 1084-1089.
%H A245676 Paul Scott, <a href="http://search.informit.com.au/documentSummary;dn=151889702719877;res=IELHSS">Convex Tangrams</a>, Australian Mathematics Teacher, 62 (2006), 2-5. Confirms a(16)=20.
%H A245676 Fu Traing Wang and Chuan-Chih Hsiung, <a href="http://www.jstor.org/stable/2303340">A Theorem on the Tangram</a>, American Mathematical Monthly, 49 (1942), 596-599.  Proves a(16)=20 and that convex polyabolos have no more than eight sides.
%H A245676 Douglas J. Durian, <a href="/A245676/a245676_1.txt">Description of shapes for n = 1..750</a>
%F A245676 a(n) = A093709(n) + A292146(n) + A292147(n) + A292148(n) + A292149(n) + A292150(n). [Wang and Hsiang (1942)] - _Douglas J. Durian_, Sep 24 2017
%e A245676 For n=3, there are two trapezoids.
%Y A245676 Strictly less than A006074 for n > 2.
%K A245676 nonn
%O A245676 1,2
%A A245676 _Eli Fox-Epstein_, Jul 29 2014
%E A245676 Definition clarified by _Douglas J. Durian_, Sep 24 2017
%E A245676 a(51) and beyond from _Douglas J. Durian_, Jan 24 2020