A353193 The row numbers of the Trithoff (tribonacci) array that don't correspond to difference sequences of other rows of the Trithoff array.

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

Author

Tanya Khovanova and PRIMES STEP Senior group, Apr 29 2022

Keywords

• nonn

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.

Examples

			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.

Cf. A000073, A000213, A001590, A136175.