A353090 Column -2 of the extended Trithoff (tribonacci) array.

0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 25, 25, 25, 26, 26, 26, 27

Offset

1,6

Comments

This column is also called the pre-seed of the Trithoff array.

This is a nondecreasing sequence containing all nonnegative integers, with some of them doubled and some tripled. The doubled numbers are the positions of the letter "c" in the tribonacci word (A003146). Correspondingly, the tripled numbers are positions of letters "a" and "b" 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). The pre-seed in the same row as n_1, n_2, and n_3 is 2n_1-n_2.

Links

Table of n, a(n) for n=1..77.

Crossrefs

Cf. A000073, A003144, A003145, A003146, A136175, A353083, A353084, A353086.

Sequence in context: A079440 A192262 A026414 * A077219 A026405 A226033

Adjacent sequences: A353087 A353088 A353089 * A353091 A353092 A353093

Keyword

nonn

Author

Tanya Khovanova and PRIMES STEP Senior group, Apr 22 2022

Status

approved