OFFSET
0,7
COMMENTS
REFERENCES
O. Gascuel (Ed.), Mathematics of Evolution and Phylogeny, Oxford University Press, 2005
LINKS
O. Gascuel, M. Hendy, A. Jean-Marie and R. McLachlan, The combinatorics of tandem duplication trees, Systematic Biology 52, 110-118, (2003).
J. Yang and L. Zhang, On Counting Tandem Duplication Trees", Molecular Biology and Evolution, Volume 21, Issue 6, (2004) 1160-1163.
FORMULA
T(n,k) = Sum_{j = 0..k+1} T(n-1,j) for n >= 4, 0 <= k <= n - 2, with T(2,0) = T(3,1) = 1, T(3,0) = 0 and T(n,k) = 0 for k >= n - 1.
T(n,k) = T(n,k-1) + T(n-1,k+1) for n >= 4, 1 <= k <= n - 2.
EXAMPLE
Triangle begins
n\k| 0 1 2 3 4 5 6 7
----------------------------------------------
.2.| 1
.3.| 0 1
.4.| 1 1 1
.5.| 2 3 3 3
.6.| 5 8 11 11 11
.7.| 13 24 35 46 46 46
.8.| 37 72 118 164 210 210 210
.9.| 109 227 391 601 811 1021 1021 1021
...
MAPLE
CROSSREFS
KEYWORD
AUTHOR
Peter Bala, Nov 27 2015
STATUS
approved