

A006074


Number of polyaboloes (or polytans): number of different shapes that can be formed with n congruent isosceles right triangles, identifying mirror images.
(Formerly M2379)


4



1, 3, 4, 14, 30, 107, 318, 1116, 3743, 13240, 46476, 166358, 596638, 2158829, 7839845
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Also called supertangrams: a generalization of tangrams.


REFERENCES

Martin Gardner, Mathematical Magic Show. Random House, NY, 1978, p. 151 (but beware errors).
T. H. O'Beirne, New Scientist, 266 (Dec 21 1961), p. 752.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Table of n, a(n) for n=1..15.
Ed Pegg, Jr., Illustrations of polyforms
Andrew Clarke, Polyaboloes
Andrew Clarke, Illustration of initial terms
Michael Keller, Counting Polyforms
Henri Picciotto, Geometric Puzzles
Miroslav Vicher, Polyforms
Eric Weisstein's World of Mathematics, Polyabolo.


CROSSREFS

Cf. A151519 (distinguishing mirror images), A245676 (number of convex polyaboloes).  George Sicherman, Nov 25 2017
Sequence in context: A080878 A110565 A057433 * A081714 A117718 A268700
Adjacent sequences: A006071 A006072 A006073 * A006075 A006076 A006077


KEYWORD

nonn,nice,hard,more


AUTHOR

N. J. A. Sloane


EXTENSIONS

Corrected values for a(8) and a(9), found by Aaron Siegel and confirmed by a Japanese puzzlist named Taro, reported by Michael Keller (Wgreview(AT)aol.com), Sep 02 2000
One more term from Vladeta Jovovic, Aug 11 2007
Link updated by William Rex Marshall, Dec 16 2009
Modified the definition (what is a "halfsquare"?) and added a(13), by George Sicherman, Apr 04 2012
a(14) from Juris Cernenoks, Sep 06 2012
a(15) from George Sicherman, Aug 02 2013


STATUS

approved



