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.
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
KEYWORD
nonn
AUTHOR
Tanya Khovanova and PRIMES STEP Senior Group, Apr 22 2022
STATUS
approved