cp's OEIS Frontend

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

%I A332440 #20 Jun 19 2020 04:42:19
%S A332440 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,
%T A332440 22,26,3,13,17,4,8,36,27,37,41,18,28,32,9,19,23
%N A332440 Three-column array read by rows: the sequence of 14 triples of the positions of the numbers 0 to 13 in sequence A332439.
%C A332440 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.
%C A332440 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}.
%F A332440 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.
%e A332440 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)).
%e A332440 The array T(n, k) in full is:
%e A332440 n\k  1   2   3
%e A332440 --------------
%e A332440 0:   0  10  14
%e A332440 1:   1   5  33
%e A332440 2:  24  34  38
%e A332440 3:  15  25  29
%e A332440 4:   6  16  20
%e A332440 5:   7  11  39
%e A332440 6:   2  30  40
%e A332440 7:  21  31  35
%e A332440 8:  12  22  26
%e A332440 9:   3  13  17
%e A332440 10:  4  8   36
%e A332440 11: 27  37  41
%e A332440 12: 18  28  32
%e A332440 13:  9  19  23
%Y A332440 Cf. A332439.
%K A332440 nonn,tabf,fini,full,easy,less
%O A332440 0,2
%A A332440 _Wolfdieter Lang_, Apr 04 2020