A354215 a(n) is the row number of the Trithoff (tribonacci) array where we can find the tail of the following sequence: apply the difference operator n times to the tribonacci sequence.

1, 2, 3, 7, 19, 29, 81, 125, 353, 161, 1545, 705, 2001, 3089, 8769, 24897, 38433, 109121, 309825, 478273, 1357953, 2096257, 5951873, 2715905

Offset: 0

Author

Tanya Khovanova and PRIMES STEP Senior group, May 19 2022

Keywords

• nonn
• more

Comments

The tribonacci sequence has a repeated pattern even, even, odd, odd. Its difference sequence alternates between even and odd. The second difference sequence consists only of odd numbers. The third or higher difference sequence consists only of even numbers. It follows that rows a(n) in the Trithoff array, for n > 2, contain all even numbers.

Examples

			Consider the tribonacci sequence A000073: 0, 0, 1, 1, 2, 4, 7, 13, .... Its first difference sequence is sequence A001590: 0, 1, 0, 1, 2, 3, 6, ... This sequence follows the tribonacci rule and its tail starting from number 3 is the second row of the Trithoff array A136175. Thus, a(1) = 2.
		

Crossrefs

Cf. A000073, A136175, A351685, A351689, A353178, A353193.