|
Search: id:A135312
|
|
|
| A135312 |
|
Number of transitive reflexive binary relations R on n labeled elements where |{y : xRy}| <= 2 for all x. |
|
+0
3
|
|
| 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)
|
|
|
OFFSET
|
0,3
|
|
|
REFERENCES
|
A. P. Heinz (1990). Analyse der Grenzen und Moeglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universitaet Freiburg, Freiburg i. Br., Germany.
|
|
LINKS
|
Alois P. Heinz (heinz(AT)hs-heilbronn.de), Dec 05 2007, Table of n, a(n) for n = 0..100
|
|
FORMULA
|
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));
|
|
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 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);
|
|
CROSSREFS
|
Cf. A135302, A006882, A000248, A007318.
Sequence in context: A115455 A149487 A057712 this_sequence A005035 A052415 A129433
Adjacent sequences: A135309 A135310 A135311 this_sequence A135313 A135314 A135315
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Alois P. Heinz (heinz(AT)hs-heilbronn.de), Dec 05 2007
|
|
|
Search completed in 0.020 seconds
|
