

A051496


Decimal expansion of probability that a point of an infinite (rooted) tree is fixed by every automorphism of the tree.


0



6, 9, 9, 5, 3, 8, 8, 7, 0, 0, 6, 0, 9, 8, 9, 2, 3, 3, 2, 1, 6, 6, 3, 1, 2, 1, 8, 6, 2, 0, 1, 4, 2, 7, 6, 7, 1, 6, 3, 6, 8, 1, 4, 5, 5, 4, 6, 3, 5, 4, 2, 1, 6, 1, 9, 8, 9, 7, 5, 9, 2, 2, 0, 3, 2, 0, 0, 4, 6, 4, 1, 9, 2, 5, 6, 2, 9, 5, 6, 1, 2, 1, 4, 8, 7, 8, 4, 8, 0, 6, 0, 2, 8, 2, 6, 5, 4, 8
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

F. Harary and E. M. Palmer derive certain functional equations and, using the methods of G. Polya (Acta Math. 68 (1937), 145 254) and R. Otter (Ann. of Math. (2) 49 (1948), 583  599; Math. Rev. 10, 53), prove that the limiting probability of a fixed point in a large random tree, whether rooted or not, is 0.6995 ...


REFERENCES

Harary, Frank; Palmer, Edgar M; The probability that a point of a tree is fixed; Math. Proc. Cambridge Philos. Soc. 85 (1979), no. 3, 407415.


LINKS

Table of n, a(n) for n=0..97.
D. J. Broadhurst and D. Kreimer, Rootedtree paper
Index entries for sequences related to trees
Index entries for sequences related to rooted trees


EXAMPLE

0.6995388700609892332166312186...


CROSSREFS

Equals \lim_{n\to\infty} A005200[n]/(n*A000081[n]) = \lim_{n\to\infty} A005201[n]/(n*A000055[n])
Sequence in context: A019902 A021147 A246709 * A330564 A195296 A273951
Adjacent sequences: A051493 A051494 A051495 * A051497 A051498 A051499


KEYWORD

nonn,cons


AUTHOR

David Broadhurst


STATUS

approved



