A007008 Chvatal conjecture for radius of graph of maximal intersecting sets.

0, 1, 1, 3, 5, 11, 22, 47, 93, 193, 386, 793, 1586, 3238, 6476, 13167, 26333, 53381, 106762, 215955, 431910, 872218, 1744436, 3518265, 7036530, 14177066, 28354132, 57079714, 114159428, 229656076, 459312152, 923471727, 1846943453, 3711565741, 7423131482

Offset: 1

Author

Daniel E. Loeb

Keywords

• nonn

References

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

Links

• Jan C. Bioch and Toshihide Ibaraki, Generating and approximating nondominated coteries, IEEE Transactions on parallel and distributed systems 6 (1995), 905-914.
• D. E. Loeb and A. Meyerowitz, The maximal intersecting family of sets graph, in H. Barcelo and G. Kalai, editors, Proceedings of the Conference on Jerusalem Combinatorics 1993. AMS series Contemporary Mathematics, 1994. [broken link]
• A. Meyerowitz, Maximal intersecting families, European J. Combin. 16 (1995), no. 5, 491-501.

Crossrefs

Cf. A000346, A007007, A001206.

Programs

PARI

A007008(n)=2^n\4-binomial(n-1,(n-1)\2)\2 \\ - M. F. Hasler, Jan 14 2014

Formula

It is conjectured that a(2n+1)=A000346(n-1) for n>0. - Ralf Stephan, May 03 2004

a(n) = round(2^(n-2)-binomial(n-1,floor((n-1)/2))/2), cf. Thm. 14 in the Loeb-Meyerowitz paper. - M. F. Hasler, Jan 14 2014