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

Author

Tanya Khovanova and PRIMES STEP Senior Group, Apr 22 2022

Keywords

• nonn

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.

Examples

			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.