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A264620
Triangle read by rows: T(n,k) (0 <= k <= n) = number of principal ideals generated by an element of rank k in the 3-tonal partition monoid on n elements.
0
1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 2, 2, 1, 1, 1, 1, 2, 3, 2, 1, 1, 0, 1, 2, 3, 3, 2, 1, 1, 0, 1, 2, 3, 4, 3, 2, 1, 1, 1, 1, 2, 4, 4, 4, 3, 2, 1, 1, 0, 1, 2, 3, 5, 5, 4, 3, 2, 1, 1, 0, 1, 2, 3, 5, 6, 5, 4, 3, 2, 1, 1, 1, 1, 2, 4, 5, 6, 7, 5, 4, 3, 2, 1, 1
OFFSET
0,13
LINKS
C. Ahmed, P. Martin, V. Mazorchuk, On the number of principal ideals in d-tonal partition monoids, arXiv preprint arXiv:1503.06718 [math.CO], 2015. See Fig. 2.
EXAMPLE
Triangle begins:
1,
0,1,
0,1,1,
1,1,1,1,
0,1,2,1,1,
0,1,2,2,1,1,
1,1,2,3,2,1,1,
0,1,2,3,3,2,1,1,
0,1,2,3,4,3,2,1,1,
1,1,2,4,4,4,3,2,1,1,
0,1,2,3,5,5,4,3,2,1,1,
0,1,2,3,5,6,5,4,3,2,1,1,
1,1,2,4,5,6,7,5,4,3,2,1,1,
...
CROSSREFS
Cf. A028289.
Sequence in context: A244925 A068914 A090824 * A302301 A277264 A259538
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Nov 30 2015
STATUS
approved