A193297 Triangle read by rows: T(n,k) = number of pairs of partitions of n that have block distance k (n >= 2, 2 <= k <= n).

1, 3, 7, 12, 28, 65, 50, 140, 325, 811, 225, 700, 1950, 4866, 12762, 1092, 3675, 11375, 34062, 89334, 244588, 5684, 20384, 68250, 227080, 714672, 1956704, 5574956, 31572, 119364, 425880, 1532790, 5360040, 17610336, 50174604, 148332645

Offset

2,2

Links

Table of n, a(n) for n=2..37.

F. Ruskey and J. Woodcock, The Rand and block distances of pairs of set partitions, Combinatorial algorithms, 287-299, Lecture Notes in Comput. Sci., 7056, Springer, Heidelberg, 2011.

Frank Ruskey, Jennifer Woodcock and Yuji Yamauchi, Counting and computing the Rand and block distances of pairs of set partitions, Journal of Discrete Algorithms, Volume 16, October 2012, Pages 236-248. - From N. J. A. Sloane, Oct 03 2012

Example

Triangle begins
1
3 7
12 28 65
50 140 325 811
225 700 1950 4866 12762
1092 3675 11375 34062 89334 244588
5684 20384 68250 227080 714672 1956704 5574956
31572 119364 425880 1532790 5360040 17610336 50174604 148332645
...

Crossrefs

Row sums give A193274.

Column k=2 gives A105479.

T(n,n) gives A152525.

Sequence in context: A182941 A063072 A007626 * A377572 A240738 A047068

Adjacent sequences: A193294 A193295 A193296 * A193298 A193299 A193300

Keyword

nonn,tabl

Author

N. J. A. Sloane, Aug 26 2011

Status

approved