A353193 - OEIS

%I #10 Jun 22 2022 20:27:42

%S 1,5,6,8,9,10,13,14,15,18,22,23,24,27,31,32,36,37,39,40,41,44,48,49,

%T 53,54,56,57,58,62,63,65,66,67,70,71,72,75,79,80,84,85,87,88,89,93,94,

%U 96,97,98,101,102,103,106,110,111,113,114,115,118,119,120,123,127,128,129,132,136,137,141,142,144

%N The row numbers of the Trithoff (tribonacci) array that don't correspond to difference sequences of other rows of the Trithoff array.

%C All positive tribonacci-like sequences are in the Trithoff array.

%C Every tribonacci-like sequence s is a difference sequence of another tribonacci-like sequence t, where t is uniquely defined. If s is an integer sequence then, t doesn't have to be an integer sequence. If t is an integer sequence, then the row number corresponding to sequence s is not in this sequence.

%C These are the Trithoff array rows that repeat a pattern: even, even, odd, odd.

%e The first row of the Trithoff array is the sequence of tribonacci numbers A000073. Its differences form sequence A001590, which is the second row of the Trithoff array. Thus, 2 is not in this sequence.

%e The tribonacci sequence, the first row of the Trithoff array, is the difference sequence of the tribonacci-like sequence A000213 divided by 2. The result is not an integer sequence. Thus, 1 is in this sequence.

%Y Complement of A353178.

%Y Cf. A000073, A000213, A001590, A136175.

%K nonn

%O 1,2

%A _Tanya Khovanova_ and PRIMES STEP Senior group, Apr 29 2022