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.

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

Author

N. J. A. Sloane, Nov 30 2015

Keywords

• nonn
• tabl

Examples

			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,
...
		

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.

Crossrefs

Cf. A028289.