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Column 0 of the extended Trithoff (tribonacci) array.
5

%I #16 May 07 2022 10:28:15

%S 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,

%T 31,32,33,34,36,37,38,39,40,42,43,44,45,46,47,49,50,51,52,53,54,56,57,

%U 58,59,60,62,63,64,65,66,67,69,70,71,73,74,75,76,77,78,80

%N Column 0 of the extended Trithoff (tribonacci) array.

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

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

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

%C 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.

%e 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.

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

%K nonn

%O 1,2

%A _Tanya Khovanova_ and PRIMES STEP Senior Group, Apr 22 2022