A348451 Triangle read by rows: T(n,k) (1 <= k <= n) is the number of 3-extensions of an n-set over all choices of 3-partitions of the n-set.

1, 2, 1, 5, 4, 1, 14, 13, 6, 1, 41, 40, 25, 9, 1, 122, 121, 90, 48, 12, 1, 365, 364, 301, 202, 78, 14, 1, 1094, 1093, 966, 747, 380, 106, 16, 1, 3281, 3280, 3025, 2559, 1571, 592, 141, 18, 1, 9842, 9841, 9330, 8362, 5864, 2755, 906, 180, 20, 1

Offset

1,2

Comments

See Lindquist et al. 1981 for precise definition.

Links

Table of n, a(n) for n=1..55.

Norman Lindquist and Gerard Sierksma, Extensions of set partitions, Journal of Combinatorial Theory, Series A 31.2 (1981): 190-198. See Table III.

Example

Triangle begins:
1,
2,1,
5,4,1,
14,13,6,1,
41,40,25,9,1,
122,121,90,48,12,1,
365,364,301,202,78,14,1,
1094,1093,966,747,380,106,16,1,
3281,3280,3025,2559,1571,592,141,18,1,
9842,9841,9330,8362,5864,2755,906,180,20,1,
...

Crossrefs

Cf. A055248.

Column 1 = A007051, column 3 = A000392.

Sequence in context: A201165 A171488 A171651 * A104710 A039598 A128738

Adjacent sequences: A348448 A348449 A348450 * A348452 A348453 A348454

Keyword

nonn,tabl

Author

N. J. A. Sloane, Oct 26 2021

Status

approved