A216813 Sum of tail length of S over all 2^n strings S consisting of n 2's and 3's.

0, 3, 6, 18, 39, 96, 201, 582, 1220, 2590, 5345, 10919, 21859, 44167, 88629, 178050, 356598, 715084, 1431514, 2866876, 5736311, 11480839, 22966942, 45949687, 91910241, 183852468, 367726473, 735517466, 1471078571, 2942286009, 5884661772, 11769583511, 23539346216, 47079214312, 94158788295

Offset: 1

Author

N. J. A. Sloane, Sep 18 2012 - Sep 21 2012, Oct 23 2012

Keywords

• nonn

Comments

"Tail length" is defined in A216730.

Links

• Benjamin Chaffin and N. J. A. Sloane, Table of n, a(n) for n = 1..40
• B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, On Curling Numbers of Integer Sequences, arXiv:1212.6102, Dec 25 2012.
• B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, On Curling Numbers of Integer Sequences, Journal of Integer Sequences, Vol. 16 (2013), Article 13.4.3.
• Index entries for sequences related to curling numbers

Crossrefs

Cf. A094005, A216730.

Formula

a(n) = A094005(n) - n*2^n.

Up to n=32, the average tail length a(n)/2^n seems to be approaching a number around 2.74.