login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; constant; graph; refs; listen; history; text; internal format)
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 Two-Dimensional Bootstrap Percolation, Prob. Th. and Related Fields 125, 195-224, 2003.

LINKS

Table of n, a(n) for n=0..101.

J. M. Borwein, R. Girgensohn, Evaluations of binomial series, Aequat. Math. 70 (2005) 25-36

A. Holroyd, Sharp Metastability Threshold for Two-Dimensional Bootstrap Percolation, arXiv:math/0206132 [math.PR], 2002.

Courtney Moen, Infinite series with binomial coefficients, Math. Mag. 64 (1) (1991) 53-55.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 14 12:28 EST 2018. Contains 318097 sequences. (Running on oeis4.)