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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).
3

%I #20 Aug 02 2014 06:14:09

%S 2,2,2,4,6,6,6,10,12,12,12,24,28,30,30,20,40,48,52,54,54,40,92,112,

%T 120,124,126,126,74,174,210,226,234,238,240,240,148,362,438,474,490,

%U 498,502,504,504,286,700,860,928,960,976,984,988,990,990,572,1448,1776,1916,1984,2016,2032,2040,2044,2046,2046

%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 Rows are partial sums of rows of A218869.

%C Final entries in rows form A027375. First column is A122536.

%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 N. J. A. Sloane, <a href="/A218870/a218870.txt">Rows 1 through 36</a>

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

%e Triangle begins:

%e [2]

%e [2, 2]

%e [4, 6, 6]

%e [6, 10, 12, 12]

%e [12, 24, 28, 30, 30]

%e [20, 40, 48, 52, 54, 54]

%e [40, 92, 112, 120, 124, 126, 126]

%e [74, 174, 210, 226, 234, 238, 240, 240]

%e [148, 362, 438, 474, 490, 498, 502, 504, 504]

%e [286, 700, 860, 928, 960, 976, 984, 988, 990, 990]

%e [572, 1448, 1776, 1916, 1984, 2016, 2032, 2040, 2044, 2046, 2046]

%e ...

%Y Cf. A216955, A122536, A027375, A218869.

%K nonn,tabl

%O 1,1

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