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A318393 Regular tetrangle where T(n,k,i) is the number of pairs of set partitions of {1,...,n} with meet of length k and join of length i. 15
1, 1, 2, 1, 1, 6, 3, 8, 6, 1, 1, 14, 7, 48, 36, 6, 56, 44, 12, 1, 1, 30, 15, 200, 150, 25, 560, 440, 120, 10, 552, 440, 140, 20, 1, 1, 62, 31, 720, 540, 90, 3640, 2860, 780, 65, 8280, 6600, 2100, 300, 15, 7202, 5632, 1920, 340, 30, 1, 1, 126, 63, 2408, 1806 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..61.

EXAMPLE

The T(3,3,1) = 8 pairs of set partitions:

  {{1},{2},{3}}  {{1,2,3}}

   {{1},{2,3}}  {{1,2},{3}}

   {{1},{2,3}}  {{1,3},{2}}

   {{1,2},{3}}  {{1},{2,3}}

   {{1,2},{3}}  {{1,3},{2}}

   {{1,3},{2}}  {{1},{2,3}}

   {{1,3},{2}}  {{1,2},{3}}

    {{1,2,3}}  {{1},{2},{3}}

Tetrangle begins:

   1   1     1       1            1

       2 1   6 3     14 7         30  15

             8 6 1   48 36 6      200 150 25

                     56 44 12 1   560 440 120 10

                                  552 440 140 20  1

MATHEMATICA

csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Union[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]];

sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];

spmeet[a_, b_]:=DeleteCases[Union@@Outer[Intersection, a, b, 1], {}]; spmeet[a_, b_, c__]:=spmeet[spmeet[a, b], c];

Table[Length[Select[Tuples[sps[Range[n]], 2], And[Length[spmeet@@#]==k, Length[csm[Union@@#]]==j]&]], {n, 6}, {k, n}, {j, k}]

CROSSREFS

Cf. A000110, A000258, A001247, A008277, A048994, A059849, A060639, A181939, A318389, A318390, A318391, A318392.

Sequence in context: A226691 A158389 A186287 * A139622 A257895 A186023

Adjacent sequences:  A318390 A318391 A318392 * A318394 A318395 A318396

KEYWORD

nonn,tabf

AUTHOR

Gus Wiseman, Aug 25 2018

STATUS

approved

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Last modified June 5 11:52 EDT 2020. Contains 334840 sequences. (Running on oeis4.)