[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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