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)

1, 3, 4, 14, 30, 107, 318, 1116, 3743, 13240, 46476, 166358, 596638, 2158829, 7839845, 28616815, 104814161, 385269397, 1420242629, 5249877583, 19452536934, 72237904034

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..22.

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

Wikimedia, Polyabolo

Crossrefs

Cf. A151519 (distinguishing mirror images), A245676 (number of convex polyaboloes). - George Sicherman, Nov 25 2017

Sequence in context: A110565 A332270 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 N. 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 "half-square"?) 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

a(16)-a(20) from John Mason, Jan 07 2022

a(21) from Aaron N. Siegel, May 17 2022

a(22) from Aaron N. Siegel, Jun 07 2022

Status

approved