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A178959
Decimal expansion of the site percolation threshold for the (3,6,3,6) Kagome Archimedean lattice.
1
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, 1, 9, 7, 6
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.
This is one of the three real roots of x^3 - 3x^2 + 1. The other roots are 1 + A332437 = 2.879385241... and -(A332438 - 3) = - 0.5320888862... . - Wolfdieter Lang, Dec 13 2022
FORMULA
Equals 1 - 2*sin(Pi/18) = 1 = 1 - 2*cos(4*Pi/9) = 1 - A130880.
EXAMPLE
0.652703644666139302296566746461370407999248645631861225527517243735868355...
MATHEMATICA
RealDigits[1 - 2 Sin[Pi/18], 10, 105][[1]] (* Alonso del Arte, Dec 22 2012 *)
PROG
(PARI) 1-2*sin(Pi/18) \\ Charles R Greathouse IV, Jan 03 2013
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
Jonathan Vos Post, Dec 22 2012
EXTENSIONS
a(98) corrected and more terms from Georg Fischer, Jun 06 2024
STATUS
approved