Template:Sequence of the Day for November 5

Intended for: November 5, 2013

Timetable

• First draft entered by Jörg Rambau on July 28, 2011 ✓
• Draft reviewed by Alonso del Arte on November 5, 2012 ✓
• Draft to be approved by October 5, 2013

Yesterday's SOTD * Tomorrow's SOTD

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A066342: Number of triangulations of the cyclic polytope

C (n, n  −  4), n   ≥   2

.

{ 1, 2, 4, 8, 14, 25, 40, 67, 102, 165, 244, 387, 562, 881, ... }

Formerly only generated by brute force in TOPCOM or the like, a surprisingly easy formula was conjectured by Santos, and finally proved in 2002 by M. Azaola and F. Santos. And closed formulas for the numbers of triangulations of other infinite classes of polytopes are rare: The Catalan numbers count the number of triangulations of

n

-gons—but that’s about it.