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A263859 Triangle read by rows: T(n,k) (n>=1, k>=0) is the number of posets with n elements and rank k (or depth k+1). 1
1, 1, 1, 1, 3, 1, 1, 8, 6, 1, 1, 20, 31, 10, 1, 1, 55, 162, 84, 15, 1, 1, 163, 940, 734, 185, 21, 1, 1, 556, 6372, 7305, 2380, 356, 28, 1, 1, 2222, 52336, 86683, 35070, 6259, 623, 36, 1, 1, 10765, 534741, 1261371, 619489, 125597, 14258, 1016, 45, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums give A000112, n >= 1.

The rank of a poset is the number of cover relations in a maximal chain.

Needs a b-file (Brinkmann and McKay give first 16 rows - see tables 6, 10, 14, ..., 54, 58). - N. J. A. Sloane, Mar 18 2017

LINKS

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

G. Brinkmann and B. D. McKay, Posets on up to 16 Points [On Brendan McKay's home page]

G. Brinkmann and B. D. McKay, Posets on up to 16 Points, Order 19 (2) (2002) 147-179.

FindStat - Combinatorial Statistic Finder, The rank of the poset.

Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Part 10 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)

EXAMPLE

Triangle begins:

1,

1,1,

1,3,1,

1,8,6,1,

1,20,31,10,1,

1,55,162,84,15,1,

1,163,940,734,185,21,1,

1,556,6372,7305,2380,356,28,1,

1,2222,52336,86683,35070,6259,623,36,1,

1,10765,534741,1261371,619489,125597,14258,1016,45,1,

...

CROSSREFS

Cf. A000112.

Sequence in context: A168216 A091698 A134380 * A124469 A094816 A097712

Adjacent sequences:  A263856 A263857 A263858 * A263860 A263861 A263862

KEYWORD

nonn,tabl,more

AUTHOR

Christian Stump, Oct 28 2015

EXTENSIONS

More terms from Brinkmann-McKay (2002) added by N. J. A. Sloane, Mar 18 2017

STATUS

approved

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Last modified February 22 05:58 EST 2018. Contains 299430 sequences. (Running on oeis4.)