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A056842 Number of polydrafters: a(n) is the number of polydrafters with n cells.

%I A056842 #34 Jul 02 2025 16:02:00
%S A056842 1,6,14,64,237,1024,4254,18664,81865,365190,1634801,7388372
%N A056842 Number of polydrafters: a(n) is the number of polydrafters with n cells.
%C A056842 See the Paterson link for the definition.
%C A056842 Restatement of the definition: A polydrafter is a polygon formed by joining 30-60-90 triangles, according to the following rules:
%C A056842 (a) Two triangles may be joined along their short legs, with their right angles touching;
%C A056842 (b) Two triangles may be joined along their long legs, with their right angles touching;
%C A056842 (c) Two triangles may be joined along their hypotenuses, in either direction;
%C A056842 (d) The short leg of triangle 1 may be joined to half of the hypotenuse of triangle 2, with the right angle of triangle 1 touching the midpoint of the hypotenuse of triangle 2.
%D A056842 Ed Pegg, Jr., Polyform puzzles, in Tribute to a Mathemagician, Peters, 2005, pp. 119-125.
%H A056842 D. Paterson, <a href="https://web.archive.org/web/20131103014511/http://mathforum.org/kb/thread.jspa?forumID=129&amp;threadID=355644&amp;messageID=1088019">Pentominos & Dodecadudes</a>
%H A056842 M. Vicher, <a href="http://www.vicher.cz/puzzle/polyforms.htm">Polyforms</a>
%H A056842 M. Vicher, <a href="http://www.vicher.cz/puzzle/polyform/tridr/triddr.html">Tridrafters</a>
%H A056842 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Polydrafter.html">Polydrafter.</a>
%e A056842 a(3) = 14 because there are 14 tridafters. The second Vicher link shows various arrangements of them.
%Y A056842 Cf. A217720 (number of one-sided polydrafters with n cells).
%Y A056842 Cf. A289137 (number of extended [two-sided] polydrafters with n cells).
%K A056842 nonn,more,hard
%O A056842 1,2
%A A056842 _James Sellers_, Aug 28 2000
%E A056842 Edited by _David Wasserman_, Dec 01 2003
%E A056842 a(10) from _George Sicherman_, Jun 23 2020
%E A056842 a(11)-a(12) from _Aaron N. Siegel_, May 13 2022