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a(n) = total number of binary sequences S of length n and curling number k (so S = XY^k) in which Y can be taken to have length 1.
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%I #5 Oct 17 2012 16:44:36

%S 2,4,8,14,28,52,104,202,402,794,1588,3152,6304,12572,25136,50198,

%T 100396,200636,401272,802260,1604488,3208416,6416832,12832482,

%U 25664962,51327702,102655278,205306104,410612208,821215304,1642430608,3284843468

%N a(n) = total number of binary sequences S of length n and curling number k (so S = XY^k) in which Y can be taken to have length 1.

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

%e Taking the alphabet to be {0,1}, the 14 sequences of length 14 are **10 (k=1), *100 (k=2), 1000 (k=3) and their complements, for a total of 2(4+2+1) = 14 (here * = 0 or 1).

%Y Cf. A217933.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Oct 17 2012