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A135312 Number of transitive reflexive binary relations R on n labeled elements where |{y : xRy}| <= 2 for all x. 6
1, 1, 4, 13, 62, 311, 1822, 11593, 80964, 608833, 4910786, 42159239, 383478988, 3678859159, 37087880754, 391641822541, 4319860660448, 49647399946049, 593217470459314, 7354718987639959, 94445777492433516, 1254196823154143191, 17198114810490326714 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

A. P. Heinz (1990). Analyse der Grenzen und Möglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universität Freiburg, Freiburg i. Br., Germany.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

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).

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.

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);

MATHEMATICA

a[n_] := SeriesCoefficient[Exp[x*Exp[x] + x^2/2], {x, 0, n}]*n!; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Feb 04 2014 *)

CROSSREFS

Cf. A135302, A006882, A000248, A007318.

Sequence in context: A057712 A208592 A213093 * A287145 A266096 A005035

Adjacent sequences:  A135309 A135310 A135311 * A135313 A135314 A135315

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 05 2007

STATUS

approved

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Last modified July 15 22:48 EDT 2019. Contains 325061 sequences. (Running on oeis4.)