A353084 Column 0 of the extended Trithoff (tribonacci) array.

1, 2, 3, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 69, 70, 71, 73, 74, 75, 76, 77, 78, 80

Offset

1,2

Comments

This column is also called the wall of the Trithoff array.

These are the positions of letters a and b in the tribonacci word.

Complement of A003146: position of letter c in the tribonacci word.

Suppose number n_1 has tribonacci representation t that ends in 1 (such numbers are in column 1 of the Trithoff array). Then its tribonacci successor n_2 has tribonacci representation t0 (such numbers are in column 2 of the Trithoff array), and the successor of the successor n_3 has tribonacci representation t00 (such numbers are in column 3 of the Trithoff array). This sequence consists of numbers n_3-n_2-n_1.

Links

Table of n, a(n) for n=1..67.

Example

The first few tribonacci numbers are 1, 2, 4, 7, 13, 24, 44. The number 23 can be represented as 13+7+2+1. Thus, its tribonacci representation is 11011. The tribonacci successor of 23 is 24+13+4+2 = 43, and the next successor is 44+24+7+4 = 79. Thus, 79 - 43 - 23 = 13 is in this sequence.

Crossrefs

Cf. A000073, A003144, A003145, A003146, A136175, A353083, A353086, A353090.

Sequence in context: A047334 A032775 A057905 * A039253 A193533 A039159

Adjacent sequences: A353081 A353082 A353083 * A353085 A353086 A353087

Keyword

nonn

Author

Tanya Khovanova and PRIMES STEP Senior Group, Apr 22 2022

Status

approved