cp's OEIS Frontend

A094005 a(n) = sum of lengths of strings that can be generated by any starting string of n 2's and 3's, using the rule described in the Comments lines.

%I A094005 #33 Jan 28 2022 01:09:13
%S A094005 2,11,30,82,199,480,1097,2630,5828,12830,27873,60071,128355,273543,
%T A094005 580149,1226626,2584822,5433676,11392986,23838396,49776503,103755527,
%U A094005 215904926,448602871,930771041,1928682932,3991605129,8251710234,17040335019,35154540729,72456654860,149208536983
%N A094005 a(n) = sum of lengths of strings that can be generated by any starting string of n 2's and 3's, using the rule described in the Comments lines.
%C A094005 Start with any initial string of n numbers s(1), ..., s(n), all = 2 or 3 (so there are 2^n starting strings). The rule for extending the string is this:
%C A094005 To get s(i+1), write the string s(1)s(2)...s(i) as xy^k for words x and y (where y has positive length) and k is maximized, i.e., k = the maximal number of repeating blocks at the end of the sequence so far (k is the curling number of s(1)s(2)...s(i)). Then s(i+1) = k if k >=2, but if k=1 you must stop (without writing down the 1).
%C A094005 a(n) = sum of final length of string, summed over all 2^n starting strings.
%C A094005 See A094004 for more terms. - _N. J. A. Sloane_, Dec 25 2012
%H A094005 F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">A Slow-Growing Sequence Defined by an Unusual Recurrence</a>, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
%H A094005 F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [<a href="http://neilsloane.com/doc/gijs.pdf">pdf</a>, <a href="http://neilsloane.com/doc/gijs.ps">ps</a>].
%H A094005 B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, <a href="http://arxiv.org/abs/1212.6102">On Curling Numbers of Integer Sequences</a>, arXiv:1212.6102, Dec 25 2012.
%H A094005 B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Sloane/sloane3.html">On Curling Numbers of Integer Sequences</a>, Journal of Integer Sequences, Vol. 16 (2013), Article 13.4.3.
%H A094005 <a href="/index/Ge#Gijswijt">Index entries for sequences related to Gijswijt's sequence</a>
%H A094005 <a href="/index/Cu#curling_numbers">Index entries for sequences related to curling numbers</a>
%F A094005 Equals A216813(n) + n*2^n. - _N. J. A. Sloane_, Sep 26 2012
%F A094005 A093369 is closely related.
%Y A094005 Cf. A090822, A093370, A093371, A094004, A216813.
%K A094005 nonn
%O A094005 1,1
%A A094005 _N. J. A. Sloane_, May 31 2004
%E A094005 a(27)-a(31) from _N. J. A. Sloane_, Sep 19 2012