A287223 Numbers of tree alignments.

0, 0, 2, 6, 22, 88, 370, 1612, 7232, 33304, 157102, 757804, 3731352, 18720504, 95519428, 494733144, 2596388976, 13783481424, 73906300822, 399722732236, 2178164438936, 11946745980632, 65898275096796, 365308080119688, 2033992114316240, 11369167905107888, 63769939599193228, 358804271821028088, 2024523256299630832

Offset: 0

Author

Julien Courtiel, May 22 2017

Keywords

• nonn

Comments

The notion of tree alignment is due to Jiang, Whang and Zhang (Alignment of trees—an alternative to tree edit).

Examples

			For n = 3, the number 6=2x3 corresponds to the number of alignments between a one-vertex tree and a two-vertices tree, or between a two-vertices tree and a one-vertex tree.
		

References

• C. Chauve, J. Courtiel and Y. Ponty, Counting, Generating and Sampling Tree Alignments, in Algorithms for Computational Biology, 2016, Lecture Notes in Computer Science, vol 9702.

Formula

G.f.: (1+sqrt(1-4*t)) * (2+8*t^2-(2-8*t) * sqrt(1-4*t)-12*t+2*sqrt(2)*R ) / (-4*t*(4*sqrt(1-4*t))) where R = sqrt((1-8*t+12*t^2)*(2*t^2+(2*t-1)*sqrt(1-4*t)+1-4*t)) (no combinatorial interpretation known).