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 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). 3

%I

%S 1,3,7,12,28,65,50,140,325,811,225,700,1950,4866,12762,1092,3675,

%T 11375,34062,89334,244588,5684,20384,68250,227080,714672,1956704,

%U 5574956,31572,119364,425880,1532790,5360040,17610336,50174604,148332645

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

%H F. Ruskey and J. Woodcock, <a href="http://webhome.cs.uvic.ca/~ruskey/Publications/RandDist/RandDist.html">The Rand and block distances of pairs of set partitions</a>, Combinatorial algorithms, 287-299, Lecture Notes in Comput. Sci., 7056, Springer, Heidelberg, 2011.

%H Frank Ruskey, Jennifer Woodcock and Yuji Yamauchi, <a href="https://doi.org/10.1016/j.jda.2012.04.003">Counting and computing the Rand and block distances of pairs of set partitions</a>, Journal of Discrete Algorithms, Volume 16, October 2012, Pages 236-248. - From _N. J. A. Sloane_, Oct 03 2012

%e Triangle begins

%e 1

%e 3 7

%e 12 28 65

%e 50 140 325 811

%e 225 700 1950 4866 12762

%e 1092 3675 11375 34062 89334 244588

%e 5684 20384 68250 227080 714672 1956704 5574956

%e 31572 119364 425880 1532790 5360040 17610336 50174604 148332645

%e ...

%Y Row sums give A193274.

%Y Column k=2 gives A105479.

%Y T(n,n) gives A152525.

%K nonn,tabl

%O 2,2

%A _N. J. A. Sloane_, Aug 26 2011

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Last modified February 16 21:46 EST 2020. Contains 331975 sequences. (Running on oeis4.)