A351685 -id:A351685 - cp's OEIS frontend

A351689 a(n) is the number in the first column of the Trithoff (tribonacci) array that starts off the row containing the tail of n times the tribonacci sequence.

1, 14, 21, 176, 220, 264, 308, 352, 2466, 2740, 3014, 3288, 3562, 3836, 4110, 4384, 4658, 4932, 5206, 5480, 5754, 37510, 39215, 40920, 42625, 44330, 46035, 47740, 49445, 51150, 52855, 54560, 56265, 57970, 59675, 61380, 63085, 64790, 66495, 68200, 69905, 71610

Offset: 1

Tanya Khovanova and PRIMES STEP Senior group, May 08 2022

nonn

The sequence is increasing.
a(n) is divisible by n.
The row number where the tail of n times tribonacci numbers appears in the Trithoff array form sequence A351685.

			Consider twice the tribonacci numbers: 0, 0, 2, 2, 4, 8, 14, 26, 48, and so on. The first few terms can be found in the first row of the Trithoff array A136175. The tail starting with 14, 26, and 48 is the seventh row of the Trithoff array. The first number in the seventh row is 14. Thus, a(2) = 14.

Cf. A000073, A136175, A351685.

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.

Original entry on oeis.org

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

Tanya Khovanova and PRIMES STEP Senior group, May 19 2022

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.

			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.

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

cp's OEIS Frontend

A351689 a(n) is the number in the first column of the Trithoff (tribonacci) array that starts off the row containing the tail of n times the tribonacci sequence.

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