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

1,1

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 Apparently unpublished.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.

Sequence in context: A192708 A233531 A320303 * A230137 A120414 A251685

Adjacent sequences: A319412 A319413 A319414 * A319416 A319417 A319418

Keyword

nonn

Author

N. J. A. Sloane, Sep 20 2018

Extensions

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

Status

approved