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A353193
The row numbers of the Trithoff (tribonacci) array that don't correspond to difference sequences of other rows of the Trithoff array.
2
1, 5, 6, 8, 9, 10, 13, 14, 15, 18, 22, 23, 24, 27, 31, 32, 36, 37, 39, 40, 41, 44, 48, 49, 53, 54, 56, 57, 58, 62, 63, 65, 66, 67, 70, 71, 72, 75, 79, 80, 84, 85, 87, 88, 89, 93, 94, 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
OFFSET
1,2
COMMENTS
All positive tribonacci-like sequences are in the Trithoff array.
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.
These are the Trithoff array rows that repeat a pattern: even, even, odd, odd.
EXAMPLE
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.
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.
CROSSREFS
Complement of A353178.
Sequence in context: A033266 A355641 A363701 * A102408 A240564 A189719
KEYWORD
nonn
AUTHOR
Tanya Khovanova and PRIMES STEP Senior group, Apr 29 2022
STATUS
approved