A316839 -id:A316839 - cp's OEIS frontend

A254990 4-bonacci word. Fixed point of morphism 0->01, 1->02, 2->03, 3->0.

0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 3

Offset: 0

Ondrej Turek, Feb 11 2015

Special case of k-bonacci word for k = 4 (see crossrefs).
The lengths of iterations S(i) are Tetranacci numbers (A000078).
Set S(0) = 0; S(1) = 0,1; S(2) = 0,1,0,2; S(3) = 0,1,0,2,0,1,0,3; for n >= 4: S(n) = S(n-1) S(n-2) S(n-3) S(n-4). The sequence is the limit S(infinity).

			The iterates are:
0
01
0102
01020103
010201030102010
01020103010201001020103010201
01020103010201001020103010201010201030102010010201030102
...

Seiichi Manyama, Table of n, a(n) for n = 0..10000
Elena Barcucci, Luc Belanger and Srecko Brlek, On tribonacci sequences, Fib. Q., 42 (2004), 314-320. See Section 4.
F. Michel Dekking, Morphisms, Symbolic Sequences, and Their Standard Forms, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.1.
O. Turek, Abelian Complexity Function of the Tribonacci Word, J. Int. Seq. 18 (2015) # 15.3.4

Cf. A000078 (lengths of iterations).
Cf. A003849 (k=2, Fibonacci word), A080843 (k=3, Tribonacci word).
Cf. A316837, A316838, A316839, A316840.

Nest[Flatten[#/.{0->{0,1},1->{0,2},2->{0,3},3->0}]&,0,7] (* Harvey P. Dale, Mar 26 2015 *)

A316837 Indices of 0's in A254990.

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 12, 14, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 123, 125, 127, 129, 131, 133, 135

Offset: 1

N. J. A. Sloane, Jul 22 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A254990, A316838, A316839, A316840.

A316838 Indices of 1's in A254990.

Original entry on oeis.org

1, 5, 9, 13, 16, 20, 24, 28, 30, 34, 38, 42, 45, 49, 53, 57, 61, 65, 69, 72, 76, 80, 84, 86, 90, 94, 98, 101, 105, 109, 113, 117, 121, 124, 128, 132, 136, 138, 142, 146, 150, 153, 157, 161, 165, 169, 173, 177, 180, 184, 188, 192, 194, 198, 202, 206, 209, 213, 217, 221, 224, 228, 232

Offset: 1

N. J. A. Sloane, Jul 22 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A254990, A316837, A316839, A316840.

A316840 Indices of 3's in A254990.

Original entry on oeis.org

7, 22, 36, 51, 63, 78, 92, 107, 115, 130, 144, 159, 171, 186, 200, 215, 230, 244, 259, 271, 286, 300, 315, 323, 338, 352, 367, 379, 394, 408, 423, 437, 452, 464, 479, 493, 508, 516, 531, 545, 560, 572, 587, 601, 616, 631, 645, 660, 672, 687, 701, 716, 724, 739, 753, 768, 780, 795, 809, 824

Offset: 1

N. J. A. Sloane, Jul 22 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A254990, A316837, A316838, A316839.

cp's OEIS Frontend

A254990 4-bonacci word. Fixed point of morphism 0->01, 1->02, 2->03, 3->0.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A316837 Indices of 0's in A254990.

Views

Author

Keywords

Links

Crossrefs

A316838 Indices of 1's in A254990.

Views

Author

Keywords

Links

Crossrefs

A316840 Indices of 3's in A254990.

Views

Author

Keywords

Links

Crossrefs