A319415 Total runs-resistance of all binary vectors of length n.

2, 6, 18, 44, 110, 216, 498, 1030, 2166, 4494, 9382, 19256, 39794, 81452, 166520, 339588, 691850, 1405540, 2856000, 5793242, 11743728, 23782412, 48133328, 97335320, 196737218, 397413614, 802432322, 1619527864, 3267496300, 6590092572, 13287437168, 26783489454

Offset: 1

Author

N. J. A. Sloane, Sep 20 2018

Keywords

• nonn

Comments

See triangle in A319411.

If we divide a(n) by 2^n, we get the average runs-resistances, which are 1, 3/2, 9/4, 11/4, 55/16, 27/8, 249/64, 515/128, 1083/256, 2247/512, 4691/1024, 2407/512, ..., or, in other words, 1, 1.500000000, 2.250000000, 2.750000000, 3.437500000, 3.375000000, 3.890625000, 4.023437500, 4.230468750, 4.388671875, 4.581054688, 4.701171875, ... How does this grow?

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..75
• Claude Lenormand, Deux transformations sur les mots, Preprint, 5 pages, Nov 17 2003. Apparently unpublished. This is a scanned copy of the version that the author sent to me in 2003.

Crossrefs

Cf. A318928, A319411.

Extensions

a(13)-a(32) from Hiroaki Yamanouchi, Sep 25 2018