OFFSET
-1,4
LINKS
Lars Blomberg, Table of n, a(n) for n = -1..5048
Alexander Berkovich and Frank G. Garvan, Some observations on Dyson's new symmetries of partitions, Journal of Combinatorial Theory, Series A 100.1 (2002): 61-93.
Freeman J. Dyson, A new symmetry of partitions, Journal of Combinatorial Theory 7.1 (1969): 56-61. See Table 2.
Freeman J. Dyson, Mappings and symmetries of partitions, J. Combin. Theory Ser. A 51 (1989), 169-180.
FORMULA
See Dyson (1969).
EXAMPLE
Triangle begins:
1,
1, 1,
2, 1, 1,
2, 2, 1, 1,
4, 3, 2, 1, 1,
5, 4, 3, 2, 1, 1,
8, 6, 5, 3, 2, 1, 1,
10, 9, 6, 5, 3, 2, 1, 1,
...
If we include negative values of the rank k, we get the following table, taken from Dyson (1969):
n\k| -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
---+---------------------------------------------------
0 | 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, ...
1 | 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, ...
2 | 2, 2, 2, 2, 2, 2, 1, 1, 0, 0, 0, 0, 0, ...
3 | 3, 3, 3, 3, 3, 2, 2, 1, 1, 0, 0, 0, 0, ...
4 | 5, 5, 5, 5, 4, 4, 3, 2, 1, 1, 0, 0, 0, ...
5 | 7, 7, 7, 6, 6, 5, 4, 3, 2, 1, 1, 0, 0, ...
6 | 11, 11, 10, 10, 9, 8, 6, 5, 3, 2, 1, 1, 0, ...
7 | 15, 14, 14, 13, 12, 10, 9, 6, 5, 3, 2, 1, 1, ...
...
Starting at column k=-1 gives the present triangle.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jan 23 2020
EXTENSIONS
a(35) and beyond from Lars Blomberg, Jan 26 2020
STATUS
approved