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A353193
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The row numbers of the Trithoff (tribonacci) array that don't correspond to difference sequences of other rows of the Trithoff array.
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2
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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