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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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4
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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| A. P. Heinz (1990). Analyse der Grenzen und Möglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universität Freiburg, Freiburg i. Br., Germany.
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..100
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FORMULA
| a(n) = Sum_{i=0..floor(n/2)} C(n,2*i) * A006882(2*i-1) * A000248(n-2*i).
a(n) = A135302(n,2).
E.g.f.: exp (x*exp(x) + x^2/2).
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EXAMPLE
| 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
| df:= proc(n) option remember; `if` (n<=1, 1, n*df(n-2)) 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(n), n=0..50);
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CROSSREFS
| Cf. A135302, A006882, A000248, A007318.
Sequence in context: A115455 A149487 A057712 * A005035 A052415 A129433
Adjacent sequences: A135309 A135310 A135311 * A135313 A135314 A135315
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KEYWORD
| nonn
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Dec 05 2007
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