A308199 The tribonacci representation of a(n) is obtained by appending 0,0 to the tribonacci representation of n (cf. A278038).

0, 4, 7, 11, 13, 17, 20, 24, 28, 31, 35, 37, 41, 44, 48, 51, 55, 57, 61, 64, 68, 72, 75, 79, 81, 85, 88, 92, 94, 98, 101, 105, 109, 112, 116, 118, 122, 125, 129, 132, 136, 138, 142, 145, 149, 153, 156, 160, 162, 166, 169, 173, 177, 180, 184, 186, 190, 193, 197, 200, 204, 206, 210, 213, 217, 221, 224, 228

Offset

0,2

Comments

From Michel Dekking, Oct 06 2019: (Start)

If w is a binary vector not containing 111, then w00 and w01 are also binary vectors not containing 111. So a(n) = A278040(n) - 1.

This sequence gives the positions of the word ab in the tribonacci word t, when t is given offset 0.

This sequence is the compound sequence A278039(A278039) of the three sequences A278039, A278040, A278041, which are the building blocks of the tribonacci world with offset 0. (End)

Links

Table of n, a(n) for n=0..67.

Formula

From Michel Dekking, Oct 06 2019: (Start)

a(n) = Sum_{k=1..n-1} d(k), where d is the tribonacci word on the alphabet {4,3,2}.

a(n) = A003144(A003144(n)) - 1. (End)

Example

u = abacabaabacaba.., then u(0)u(1) = ab, u(4)u(5) = ab, u(7)u(8) = ab, u(11)u(12) = ab.

Crossrefs

Cf. A278038, A278039, A278040, A278041, A308200.

Essentially partial sums of A276789.

Sequence in context: A091855 A191404 A288374 * A310722 A092403 A219051

Adjacent sequences: A308196 A308197 A308198 * A308200 A308201 A308202

Keyword

nonn,base

Author

N. J. A. Sloane, Jun 23 2019

Status

approved