OFFSET
2,4
COMMENTS
See Figure 3(a) in Gascuel et al. (2003).
REFERENCES
O. Gascuel (Ed.), Mathematics of Evolution and Phylogeny, Oxford University Press, 2005
LINKS
O. Gascuel, M. Hendy, A. Jean-Marie and R. McLachlan, (2003) The combinatorics of tandem duplication trees, Systematic Biology 52, 110-118.
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 >= 3, 0 <= k <= n - 2, with T(2,0) = 1 and T(n,k) = 0 for k >= n - 1.
T(n,k) = T(n,k-1) + T(n-1,k+1) for n >= 3, 1 <= k <= n - 2.
EXAMPLE
Triangle begins
n\k| 0 1 2 3 4 5 6 7
---+---------------------------------------
2 | 1
3 | 1 1
4 | 2 2 2
5 | 4 6 6 6
6 | 10 16 22 22 22
7 | 26 48 70 92 92 92
8 | 74 144 236 328 420 420 420
9 | 218 454 782 1202 1622 2042 2042 2042
...
MAPLE
CROSSREFS
KEYWORD
AUTHOR
Peter Bala, Nov 27 2015
STATUS
approved