

A086463


Decimal expansion of Pi^2/18.


9



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

0,1


COMMENTS

n steps of bootstrap percolation on an s X s grid with random initial condition of density p, Holroyd (2003) showed that the asymptotic threshold occurs such that Limit[p approaches 0][s approaches infinity] = (1/18)(pi^2) [From Mathworld Bootstrap Percolation article] [Jonathan Vos Post, Aug 25 2010]
The sequence of repeating coefficients [1,1,2,1,1,2] in the sum in the formula section, is equal to the 6th column in A191898. [Mats Granvik, Mar 19 2012]


REFERENCES

A. Holroyd, Sharp Metastability Threshold for TwoDimensional Bootstrap Percolation, Prob. Th. and Related Fields 125, 195224, 2003.


LINKS

Table of n, a(n) for n=0..101.
J. M. Borwein, R. Girgensohn, Evaluations of binomial series, Aequat. Math. 70 (2005) 2536
A. Holroyd, Sharp Metastability Threshold for TwoDimensional Bootstrap Percolation, arXiv:math/0206132 [math.PR], 2002.
Courtney Moen, Infinite series with binomial coefficients, Math. Mag. 64 (1) (1991) 5355.
Eric Weisstein's World of Mathematics, Central Binomial Coefficient
Eric W. Weisstein, Bootstrap Percolation


FORMULA

Sum[1/n^2/Binomial[2n,n], {n,Infinity}].
Pi^2/18 = A013661/3 = Sum[1/(i+0)^2  1/(i+1)^2  2/(i+2)^2  1/(i+3)^2 + 1/(i+4)^2 + 2/(i+5)^2, {i =1, 7, 13, 19, 25,.. infinity, stride of 6}]. [Mats Granvik, Mar 19 2012]


EXAMPLE

0.54831...


MATHEMATICA

RealDigits[Pi^2/18, 10, 120][[1]] (* Harvey P. Dale, Aug 14 2011 *)


PROG

(PARI) Pi^2/18 \\ Charles R Greathouse IV, Mar 20 2012


CROSSREFS

Cf. A073010, A073016, A086464.
Sequence in context: A051553 A203139 A184085 * A279916 A021952 A198579
Adjacent sequences: A086460 A086461 A086462 * A086464 A086465 A086466


KEYWORD

nonn,easy,cons


AUTHOR

Eric W. Weisstein, Jul 21 2003


STATUS

approved



