[seqfan] Comments to sequences concerning "forests"

Gottfried Helms Annette.Warlich at t-online.de
Fri Dec 26 17:04:24 CET 2008


Hi -

triggered by a discussion in sci.math about the best definition
for the "matrix-power"

A^B = exp(log(A)*B)

or

A^B = exp(B * log(A))

I fiddled with the tetration of the Pascal-matrix and got some nice
and interesting results (and some open questions...)

I found connections to
A000248	Number of forests with n nodes and height at most 1.
A000949	Number of forests with n nodes and height at most 2.
A000950	Number of forests with n nodes and height at most 3.
A000951	Number of forests with n nodes and height at most 4.
		
A000272	Number of trees on n labeled nodes: n^(n-2).


	http://www.research.att.com/~njas/sequences/A000248
	http://www.research.att.com/~njas/sequences/A000949
	http://www.research.att.com/~njas/sequences/A000950
	http://www.research.att.com/~njas/sequences/A000951
	http://www.research.att.com/~njas/sequences/A000272

See a short treatize in draft-state

     http://go.helms-net.de/math/tetdocs/PascalMatrixTetrated.pdf

Gottfried




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