A324035 Irregular triangle read by rows of the entries of the Collatz tree A088975 modulo 6, starting with entry 8 == 2 (mod 6).

2, 4, 5, 2, 4, 4, 3, 2, 3, 2, 0, 4, 0, 4, 0, 1, 2, 0, 1, 2, 0, 2, 4, 0, 2, 4, 0, 4, 5, 2, 0, 4, 5, 2, 0, 5, 2, 4, 4, 0, 5, 2, 4, 4, 0, 4, 4, 5, 2, 3, 2, 0, 4, 4, 5, 2, 3, 2, 0, 5, 2, 3, 2, 4, 4, 0, 4, 0, 3, 2, 3, 2, 4, 4, 0, 4

Offset: 0

Author

Wolfdieter Lang, Feb 14 2019

Keywords

• nonn
• tabf
• easy

Comments

The length of row l of this irregular triangle is A005186(n+3), n >= 0.

The entries of the Collatz tree A088975 modulo 6 are interesting because each 4 (mod 6) entry belongs to a vertex with outdegree 2 and all other vertices have outdegree 1. See a comment in A088975. The root 8 is chosen because the vertex 4 of the preceding level does not obey this rule (otherwise a tree repetiton would occur).

The number of entries of level n congruent to 4 modulo 6 are given by A176866(n+4), for n >= 0.

Examples

			The irregular triangle T begins:
n\k   1 2 3 4 5 6 7 8 9 10 11 12 13 14  15 16 17 18 ...   A005186(n+3)
0:    2                                                         1
1:    4                                                         1
2:    5 2                                                       2
3:    4 4                                                       2
4:    3 2 3 2                                                   4
5:    0 4 0 4                                                   4
6:    0 1 2 0 1 2                                               6
7:    0 2 4 0 2 4                                               6
8:    0 4 5 2 0 4 5 2                                           8
9:    0 5 2 4 4 0 5 2 4  4                                     10
10:   0 4 4 5 2 3 2 0 4  4  5  2  3  2                         14
11:   0 5 2 3 2 4 4 0 4  0  3  2  3  2  4  4   0   4           18
...
		

Crossrefs

Cf. A005186, A088975, A176866.

Formula

T(n, k) = A088975(n+3, k) (mod 6), k = 1..A005186(n+3), n >= 0.