A218869 Triangle read by rows: T(n,k) = number of aperiodic binary sequences of length n with curling number k (1 <= k <= n).

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

Offset

1,1

Comments

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

Row sums are A027375. First column is A122536.

It appears that reversed rows converge to A155559. - Omar E. Pol, Nov 20 2012

Links

Table of n, a(n) for n=1..78.

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.

John P. Linderman, Rows 1 through 64 (Rows 1 through 36 were computed by N. J. A. Sloane)

Index entries for sequences related to curling numbers

Example

Triangle begins:
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, 100, 36, 16, 8, 4, 2, 0,
148, 214, 76, 36, 16, 8, 4, 2, 0,
286, 414, 160, 68, 32, 16, 8, 4, 2, 0,
572, 876, 328, 140, 68, 32, 16, 8, 4, 2, 0,
...

Crossrefs

Cf. A216955, A122536, A027375, A218870.

Sequence in context: A201396 A005881 A218875 * A144458 A098268 A330347

Adjacent sequences: A218866 A218867 A218868 * A218870 A218871 A218872

Keyword

nonn,tabl

Author

N. J. A. Sloane, Nov 07 2012

Status

approved