

A178959


Decimal expansion of the site percolation threshold for the (3,6,3,6) Kagome Archimedean lattice.


0



6, 5, 2, 7, 0, 3, 6, 4, 4, 6, 6, 6, 1, 3, 9, 3, 0, 2, 2, 9, 6, 5, 6, 6, 7, 4, 6, 4, 6, 1, 3, 7, 0, 4, 0, 7, 9, 9, 9, 2, 4, 8, 6, 4, 5, 6, 3, 1, 8, 6, 1, 2, 2, 5, 5, 2, 7, 5, 1, 7, 2, 4, 3, 7, 3, 5, 8, 6, 8, 3, 5, 5, 7, 2, 1, 9, 7, 0, 5, 2, 9, 1, 5, 6, 9, 6, 6, 7, 7, 3, 6, 8, 5, 2, 0, 0, 8, 5, 2
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OFFSET

0,1


COMMENTS

Consider an infinite graph where vertices are selected with probability p. The site percolation threshold is a unique value p_c such that if p > p_c an infinite connected component of selected vertices will almost surely exist, and if p < p_c an infinite connected component will almost surely not exist. This sequence gives p_c for the (3,6,3,6) Kagome Archimedean lattice.


REFERENCES

Sykes, M. F.; J. W. Essam (1964). "Exact critical percolation probabilities for site and bond problems in two dimensions". Journal of Mathematical Physics (N.Y.) 5 (8): 11171127. Bibcode 1964JMP.....5.1117S. doi:10.1063/1.1704215.


LINKS

Table of n, a(n) for n=0..98.
Wikipedia, Percolation threshold


FORMULA

1  2*sin(Pi/18).


EXAMPLE

0.6527036446661393...


MATHEMATICA

RealDigits[1  2 Sin[Pi/18], 10, 105][[1]] (* Alonso del Arte, Dec 22 2012 *)


PROG

(PARI) 12*sin(Pi/18) \\ Charles R Greathouse IV, Jan 03 2013


CROSSREFS

Cf. A174849.
Sequence in context: A197265 A198107 A004554 * A266998 A021609 A140684
Adjacent sequences: A178956 A178957 A178958 * A178960 A178961 A178962


KEYWORD

nonn,cons,easy


AUTHOR

Jonathan Vos Post, Dec 22 2012


STATUS

approved



