A332440 Three-column array read by rows: the sequence of 14 triples of the positions of the numbers 0 to 13 in sequence A332439.

0, 10, 14, 1, 5, 33, 24, 34, 38, 15, 25, 29, 6, 16, 20, 7, 11, 39, 2, 30, 40, 21, 31, 35, 12, 22, 26, 3, 13, 17, 4, 8, 36, 27, 37, 41, 18, 28, 32, 9, 19, 23

Offset: 0

Author

Wolfdieter Lang, Apr 04 2020

Keywords

• nonn
• tabf
• fini
• full
• easy
• less

Comments

A332439 gives the vertex labels of a directed Euler tour (directed Eulerian cycle) on the regular 14-gon. Every label k from {0,1, ..., 13} for the vertices V^{(14)}_k (nodes) of this regular digraph of degree 6 appears thrice in this Euler tour of length 42.

The three positions of k in the tour A332439 = T are T(a(3*k)), T(a(3*k+1)) and T(a(3*k+2)), for k from {0,1, ..., 13}.

Examples

			The label 0 (vertex V^{14}_0 = (r, 0) in Cartesian coordinates) appears at positions 0, 10 and 14 in the Euler tour A332439. This means that starting at V^{14}_0, one reaches this vertex again after 10 steps (a closed directed trail, using only distinct arrows). But no periodicity has been reached yet, and after another four steps one visits V^{14}_0 again (position 14), and finally periodicity is reached after another 28 steps (position 42 == 0 (mod 14)).
The array T(n, k) in full is:
n\k  1   2   3
--------------
0:   0  10  14
1:   1   5  33
2:  24  34  38
3:  15  25  29
4:   6  16  20
5:   7  11  39
6:   2  30  40
7:  21  31  35
8:  12  22  26
9:   3  13  17
10:  4  8   36
11: 27  37  41
12: 18  28  32
13:  9  19  23
		

Crossrefs

Cf. A332439.

Formula

T(n, k), for n = 0, 1, ..., 13 and k = 1, 2, and 3, is the first, second and third appearance of n in A332439.