|
Search: id:A086521
|
|
|
| A086521 |
|
Number of tandem duplication trees on n duplicated genes. For n > 2, 2a(n) is the number of rooted tandem duplication trees. |
|
+0
1
|
|
| 1, 1, 3, 11, 46, 210, 1021, 5202, 27477, 149324, 830357, 4705386, 27087106, 158019030, 932390694, 5555902302, 33391080001, 202196156448, 1232550473918, 7558030268270, 46592437224093, 288599067239678, 1795348952256896
(list; graph; listen)
|
|
|
OFFSET
|
2,3
|
|
|
REFERENCES
|
O. Gascuel, M. Hendy, A. Jean-Marie and R.McLachlan, (2003) The combinatorics of tandem duplication trees, Systematic Biology 52, 110-118.
|
|
LINKS
|
Author?, More information
|
|
FORMULA
|
a(n)=b(n+1, n-1), where b(n, 0)=b(n-1, 0)+b(n-1, 1); b(n, k)=b(n-1, k+1)+b(n, k-1), for k=1, ..., n-2; with initial values b(2, 0)=1, b(3, 0)=0, b(3, 1)=1.
|
|
EXAMPLE
|
a(5)=11, so there are 11 binary leaf labeled trees on 5 duplicate genes. As there are 15 binary leaf labeled trees, this means not all binary leaf labeled trees can represent a gene duplication tree.
|
|
CROSSREFS
|
Sequence in context: A151141 A155134 A006605 this_sequence A046996 A129579 A030814
Adjacent sequences: A086518 A086519 A086520 this_sequence A086522 A086523 A086524
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Michael D Hendy (m.hendy(AT)massey.ac.nz), Sep 10 2003
|
|
EXTENSIONS
|
More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Mar 11 2005
|
|
|
Search completed in 0.002 seconds
|
