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Search: id:A135312
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| A135312 |
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Number of transitive reflexive binary relations R on n labeled elements where |{y : xRy}| <= 2 for all x. |
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+0
3
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| 1, 1, 4, 13, 62, 311, 1822, 11593, 80964, 608833, 4910786, 42159239, 383478988, 3678859159, 37087880754, 391641822541, 4319860660448, 49647399946049, 593217470459314, 7354718987639959, 94445777492433516, 1254196823154143191
(list; graph; listen)
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OFFSET
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0,3
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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 (heinz(AT)hs-heilbronn.de), Dec 05 2007, Table of n, a(n) for n = 0..100
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FORMULA
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a(n) = A135302(n,2); e.g.f.: t(x) = exp(x*exp(x)+x^2/2); a(n) = sum_{i=0..floor(n/2)} (binomial(n,i+i)*A006882(i+i-1)*A000248(n-i-i));
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EXAMPLE
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a(2)=4 because there are 4 relations of the given kind for 2 elements: 1R1, 2R2; 1R1, 2R2, 1R2; 1R1, 2R2, 2R1; 1R1, 2R2, 1R2, 2R1;
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MAPLE
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df := proc(n) option remember; if n <= 1 then 1 else n*df(n-2); fi; end; u := proc(n) add (binomial(n, i)*(n-i)^i, i=0..n); end; a := proc(n) add (binomial(n, i+i)*df(i+i-1)*u(n-i-i), i=0..floor(n/2)); end; seq(a(i), i=0..50);
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CROSSREFS
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Cf. A135302, A006882, A000248, A007318.
Adjacent sequences: A135309 A135310 A135311 this_sequence A135313 A135314 A135315
Sequence in context: A115455 A149487 A057712 this_sequence A005035 A052415 A129433
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Dec 05 2007
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