A216955 - OEIS

A216955

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

2, 2, 2, 4, 2, 2, 6, 6, 2, 2, 12, 12, 4, 2, 2, 20, 26, 10, 4, 2, 2, 40, 52, 20, 8, 4, 2, 2, 74, 110, 38, 18, 8, 4, 2, 2, 148, 214, 82, 36, 16, 8, 4, 2, 2, 286, 438, 164, 70, 34, 16, 8, 4, 2, 2, 572, 876, 328, 140, 68, 32, 16, 8, 4, 2, 2, 1124, 1762, 660, 286, 134, 66, 32, 16, 8, 4, 2, 2, 2248, 3524, 1320, 572, 268, 132, 64, 32, 16, 8, 4, 2, 2

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OFFSET

1,1

COMMENTS

For definition of curling number see A216730.

"Binary" sequence means two-valued. It doesn't matter if the alphabet is {0,1} or {2,3}.

It appears that reversed rows converge to the sequence formed by the even terms of A090129. - Omar E. Pol, Nov 20 2012

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..5460

Benjamin Chaffin, John P. Linderman, N. J. A. Sloane and Allan Wilks, First 104 rows of A216955

B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, On Curling Numbers of Integer Sequences, arXiv:1212.6102, Dec 25 2012.

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

EXAMPLE

Triangle begins:

2, 2,

4, 2, 2,

6, 6, 2, 2,

12, 12, 4, 2, 2,

20, 26, 10, 4, 2, 2,

40, 52, 20, 8, 4, 2, 2,

74, 110, 38, 18, 8, 4, 2, 2,

148, 214, 82, 36, 16, 8, 4, 2, 2,

286, 438, 164, 70, 34, 16, 8, 4, 2, 2,