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

Author

N. J. A. Sloane, Jun 23 2019

Keywords

• nonn
• base

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)

Examples

			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.

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)