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EXAMPLE
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. 1: 1
. 2: 2 3
. 3: 4 1 5
. 4: 6 2 3 7
. 5: 8 4 1 5 9
. 6: 10 6 2 3 7 11
. 7: 12 8 4 1 5 9 13
. 8: 14 10 6 2 3 7 11 15
. 9: 16 12 8 4 1 5 9 13 17
. 10: 18 14 10 6 2 3 7 11 15 19
. 11: 20 16 12 8 4 1 5 9 13 17 21
. 12: 22 18 14 10 6 2 3 7 11 15 19 23 .
Removing the first and last entries from each row gives the same tree back again.
Eric Angelini's original posting to the Sequence Fans mailing list gave a different sequence, as follows:
..................................1,
.................................2,3,
................................4,1,5,
...............................6,2,3,7,
..................................8,
..............................9,4,1,5,10,
............................11,6,2,3,7,12,
................................13,14,
...............................15,8,16,
...........................17,9,4,1,5,10,18,
.........................19,11,6,2,3,7,12,20,
........................21,13,8,4,1,5,9,14,22,
.............................23,15,16,24,
.................................25,
...........................26,17,10,18,27,
......................28,19,11,6,2,3,7,12,20,29,
.....................30,21,13,8,4,1,5,9,14,22,31,
..........................32,23,15,16,24,33,
................................34,35,
..............................36,25,37,
........................38,26,17,10,18,27,39,
...................40,28,19,11,6,2,3,7,12,20,29,41,
..................42,30,21,13,8,4,1,5,9,14,22,31,43,
................44,32,23,15,10,6,2,3,7,11,16,24,33,45,
...............46,34,25,17,12,8,4,1,5,9,13,18,26,35,47,
.......................48,36,27,19,20,28,37,49,
.............50,38,29,21,14,10,6,2,3,7,11,15,22,30,39,51,
............52,40,31,23,16,12,8,4,1,5,9,13,17,24,32,41,53,
.....................54,42,33,25,18,26,34,43,55,
.............................56,44,45,57,
.................................58,
.....................................
The idea is that the n-th term is equal to the number of terms in the n-th row of the tree. This lovely sequence (whose precise definition is not clear to me) is not yet in the OEIS. (End)
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