OFFSET
0,3
COMMENTS
For j >= 1, the sequence a(j,1) begins
2, 3, 2, 5, 4, 4, 8, 9, 8, 8, 32, 8, 64, 16, 16, 17, 16, 16, 512, 16, 64, 64, 2048, 16, 1024, 128, 512, 32, 16384, 32, ...
Conjecture: a(2^m,1) = 2^m + 1 for all m > 1.
Conjecture: a(m,1) is a power of 2 whenever m is not a power of 2.
The sequence of the number of distinct values in the n-th row begins 1, 2, 3, 2, 5, 4, 4, 4, 9, 4, 8, 4, 8, 4, 10, 6, 17, 6, 10, ... - Peter Kagey, Jul 03 2022
LINKS
Peter Kagey, Rows n = 0..12 of the triangle, flattened
EXAMPLE
Table begins:
n\k | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
----+-----------------------------------------------
0 | 1;
1 | 1, 2;
2 | 1, 3, 3, 2;
3 | 1, 2, 2, 1, 2, 1, 1, 2;
4 | 1, 5, 5, 4, 5, 3, 4, 5, 5, 4, 3, 5, 4, 5, 5, 2;
... | ...
a(5,13) = 4 because 13 is 01101 in binary; the sequence of first differences is 01101, 10111, 11000, 01001, 11011, ...; and 10111 is the same necklace as 11011.
CROSSREFS
KEYWORD
AUTHOR
Peter Kagey, Jun 26 2022
STATUS
approved