A006074 Number of polyaboloes (or polytans): number of different shapes that can be formed with n congruent isosceles right triangles, identifying mirror images.
1, 3, 4, 14, 30, 107, 318, 1116, 3743, 13240, 46476, 166358, 596638, 2158829, 7839845, 28616815, 104814161, 385269397, 1420242629, 5249877583, 19452536934, 72237904034
Offset: 1
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
- 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
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
Comments