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A332440
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Three-column array read by rows: the sequence of 14 triples of the positions of the numbers 0 to 13 in sequence A332439.
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1
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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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}.
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LINKS
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FORMULA
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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.
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EXAMPLE
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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
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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
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CROSSREFS
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KEYWORD
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nonn,tabf,fini,full,easy,less
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AUTHOR
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STATUS
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approved
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