A122536 -id:A122536 - cp's OEIS frontend

A211966 Number of binary sequences of length 2n and curling number 1.

2, 6, 20, 74, 286, 1124, 4460, 17768, 70930, 283440, 1133200, 4531686, 18124522, 72493652, 289965744, 1159845258, 4639345612, 18557311624, 74229104872, 296916136278, 1187663978718, 4750654782144, 19002616863186, 76010462922018

Offset: 1

Omar E. Pol, Nov 28 2012

nonn

Equivalently, number of binary sequences of length 2n with no initial repeats (see A122536).

B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, On Curling Numbers of Integer Sequences, arXiv:1212.6102
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

Bisection of A122536.

Cf. A093371, A211965, A216955, A216958.

a(n) = 2*A093371(2n) = A093371(2n+1) = A211965(n+1)/2.

A216957 a(1)=2; for n > 1, a(n) = 2^(n-2) + (1/(2n-2)) * Sum_{ d divides n-1 } phi(2d)*2^((n-1)/d).

Original entry on oeis.org

2, 2, 4, 6, 12, 20, 40, 74, 148, 286, 568, 1118, 2228, 4412, 8788, 17480, 34836, 69392, 138388, 275942, 550560, 1098516, 2192572, 4376666, 8738324, 17448308, 34845304, 69594398, 139011816, 277691852, 554767744, 1108378658, 2214594580, 4425117884, 8842583584, 17670722600, 35314182976, 70576759892, 141055781836

Offset: 1

N. J. A. Sloane, Sep 26 2012

nonn

N. J. A. Sloane, Table of n, a(n) for n = 1..1000

Different from, but easily confused with, A003000 and A122536.

with(numtheory);
f:=n-> if n=1 then 2 else 2^(n-2) + (1/(2*n-2)) * add(phi(2*d)*2^((n-1)/d), d in divisors(n-1)); fi;

A217212 Number of sequences of 2's and 3's of length n with curling number 3.

Original entry on oeis.org

0, 0, 2, 2, 4, 10, 20, 38, 82, 164, 328, 660, 1320, 2640, 5304, 10596, 21192, 42424, 84848, 169668, 339428, 678856, 1357712, 2715548, 5431096, 10862192, 21724746, 43449380, 86898760, 173798220, 347596440, 695192670

Offset: 1

N. J. A. Sloane, Oct 01 2012

nonn

Column 3 of A216955. Cf. A122536, A217211.

cp's OEIS Frontend

A211966 Number of binary sequences of length 2n and curling number 1.

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A216957 a(1)=2; for n > 1, a(n) = 2^(n-2) + (1/(2n-2)) * Sum_{ d divides n-1 } phi(2d)*2^((n-1)/d).

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A217212 Number of sequences of 2's and 3's of length n with curling number 3.

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