A217212 -id:A217212 - cp's OEIS frontend

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

Offset: 1

N. J. A. Sloane, Sep 26 2012

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

			Triangle begins:
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,
...

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

Leading columns are A122536 (or A093371), A217211, A217212. Cf. A216956, A217943.

Extended to 104 rows by N. J. A. Sloane, Nov 15 2012

A217211 Number of binary sequences of length n with curling number 2.

Original entry on oeis.org

0, 2, 2, 6, 12, 26, 52, 110, 214, 438, 876, 1762, 3524, 7084, 14144, 28360, 56720, 113542, 227084, 454448, 908804, 1818168, 3636336, 7273614, 14547228, 29096678, 58192994, 116390424, 232780848, 465569860, 931139720, 1862297158, 3724592874, 7449221168, 14898442336, 29796952652, 59593905304

Offset: 1

N. J. A. Sloane, Oct 01 2012

nonn

N. J. A. Sloane, Table of n, a(n) for n = 1..104 [Entries up through 51 found by direct search (see triangle A216955), later entries obtained from a recurrence.]

Column 2 of A216955. Cf. A122536, A217212.

a(33)-a(37) from Allan Wilks, Oct 06 2012

cp's OEIS Frontend

A216955 Triangle read by rows: T(n,k) (n>=1, 1<=k<=n) = number of binary sequences of length n and curling number k.

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