A002661 Least integer having Radon random number n. (Formerly M0723 N0270)

1, 2, 3, 5, 10, 18, 35, 63, 126, 231, 462, 858, 1716, 3218, 6435, 12155, 24310, 46189, 92378, 176358, 352716, 676039, 1352078, 2600150, 5200300, 10029150, 20058300, 38779380, 77558760, 150270098, 300540195, 583401555, 1166803110, 2268783825, 4537567650

Offset

1,2

Comments

Old name was "From Radon's theorem".

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Matthew House, Table of n, a(n) for n = 1..3328

J. Eckhoff, Der Satz von Radon in konvexen Produktstrukturen II, Monat. f. Math., 73 (1969), 7-30.

Michael Hendriksen and Nils Kapust, On the Comparison of Incompatibility of Split Systems Across Different Numbers of Taxa, Bull. of Math. Biology (2021) Vol. 83, Art. No. 78.

Formula

a(n) = ceiling(binomial(n + 1, floor((n + 1) / 2)) / 2). - Sean A. Irvine, May 21 2014; corrected by Matthew House, Jul 29 2015

Mathematica

Table[Ceiling[Binomial[n + 1, Floor[(n + 1)/2]]/2], {n, 40}] (* Vincenzo Librandi, Jul 30 2015 *)

Prog

(Magma) [Ceiling(Binomial(n+1, Floor((n+1)/2))/2): n in [1..40]]; // Vincenzo Librandi, Jul 30 2015
(PARI) vector(40, n, ceil(binomial(n + 1, floor((n + 1) / 2)) / 2)) \\ Michel Marcus, Jul 30 2015

Crossrefs

Sequence in context: A081172 A318301 A030032 * A216959 A065053 A237250

Adjacent sequences: A002658 A002659 A002660 * A002662 A002663 A002664

Keyword

nonn

Author

N. J. A. Sloane

Extensions

New name and more terms from Sean A. Irvine, May 21 2014

Status

approved