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Triangle read by rows: T(n,k) = number of aperiodic binary sequences of length n with curling number k (1 <= k <= n).
6

%I #31 Aug 02 2014 06:21:33

%S 2,2,0,4,2,0,6,4,2,0,12,12,4,2,0,20,20,8,4,2,0,40,52,20,8,4,2,0,74,

%T 100,36,16,8,4,2,0,148,214,76,36,16,8,4,2,0,286,414,160,68,32,16,8,4,

%U 2,0,572,876,328,140,68,32,16,8,4,2,0,1124,1722,640,276,132,64,32,16,8,4,2,0

%N Triangle read by rows: T(n,k) = number of aperiodic binary sequences of length n with curling number k (1 <= k <= n).

%C S is aperiodic if it is not of the form S = T^m with m > 1.

%C Row sums are A027375. First column is A122536.

%C It appears that reversed rows converge to A155559. - _Omar E. Pol_, Nov 20 2012

%H 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 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 John P. Linderman, <a href="/A218869/a218869.txt">Rows 1 through 64</a> (Rows 1 through 36 were computed by _N. J. A. Sloane_)

%H <a href="/index/Cu#curling_numbers">Index entries for sequences related to curling numbers</a>

%e Triangle begins:

%e 2,

%e 2, 0,

%e 4, 2, 0,

%e 6, 4, 2, 0,

%e 12, 12, 4, 2, 0,

%e 20, 20, 8, 4, 2, 0,

%e 40, 52, 20, 8, 4, 2, 0,

%e 74, 100, 36, 16, 8, 4, 2, 0,

%e 148, 214, 76, 36, 16, 8, 4, 2, 0,

%e 286, 414, 160, 68, 32, 16, 8, 4, 2, 0,

%e 572, 876, 328, 140, 68, 32, 16, 8, 4, 2, 0,

%e ...

%Y Cf. A216955, A122536, A027375, A218870.

%K nonn,tabl

%O 1,1

%A _N. J. A. Sloane_, Nov 07 2012