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Search: id:A135302
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| A135302 |
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Square array of numbers A(n,k) (n>=0, k>=0) of transitive reflexive early confluent binary relations R on n labeled elements where |{y : xRy}| <= k for all x, read by antidiagonals. Early confluency means that (xRy AND xRz) implies (yRz OR zRy) for all z, y, z. |
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+0
3
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| 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 4, 1, 1, 0, 1, 13, 4, 1, 1, 0, 1, 62, 26, 4, 1, 1, 0, 1, 311, 168, 26, 4, 1, 1, 0, 1, 1822, 1416, 243, 26, 4, 1, 1, 0, 1, 11593, 13897, 2451, 243, 26, 4, 1, 1, 0, 1, 80964, 153126, 29922, 2992, 243, 26, 4, 1, 1, 0, 1, 608833, 1893180, 420841
(list; table; graph; listen)
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OFFSET
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0,13
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COMMENT
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Table begins:
1, 1, 1, 1, ...
0, 1, 1, 1,
0, 1, 4, 4,
0, 1, 13, 26,
0, 1, 62, 168,
0, 1, 311, 1416,
...
The diagonal is sequence A052880.
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REFERENCES
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A. P. Heinz (1990). Analyse der Grenzen und Moeglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universitaet Freiburg, Freiburg i. Br., Germany.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..323
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FORMULA
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E.g.f. of column k=0: t_0(x)=1; e.g.f. of column k>0: t_k(x)=exp(sum_{m=1..k}(x^m/m!*t_{k-m}(x))).
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MAPLE
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t := proc(k) option remember; if k<0 then 0 else unapply(exp(sum('x^m/m!*t(k-m)(x)', 'm'=1..k)), x) fi; end; A := proc(n, k) option remember; coeff(series(t(k)(x), x=0, n+1), x, n)*n!; end; seq(seq(A(d-i, i), i=0..d), d=0..15);
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CROSSREFS
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Cf. A052880.
Sequence in context: A117414 A085639 A158972 this_sequence A128760 A057884 A016684
Adjacent sequences: A135299 A135300 A135301 this_sequence A135303 A135304 A135305
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KEYWORD
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nonn,tabl
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Dec 04 2007
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