

A156816


Decimal expansion of the positive root of the equation 13x^4  7x^2  581 = 0.


0



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

1,1


COMMENTS

This constant approximates the connective constant of the square lattice, which is known only numerically, but "no derivation or explanation of this quartic polynomial is known, and later evidence has raised doubts about its validity" [Bauerschmidt et al, 2012, p. 4].  Andrey Zabolotskiy, Dec 26 2018


REFERENCES

N. Madras and G. Slade, The SelfAvoiding Walk (Boston: Birkhauser), 1993.


LINKS

Table of n, a(n) for n=1..105.
Roland Bauerschmidt, Hugo DuminilCopin, Jesse Goodman, Gordon Slade, Lectures on SelfAvoiding Walks, arXiv:1206.2092 [math.PR], 2012.
M. BousquetMÃ©lou, A. J. Guttmann and I. Jensen, Selfavoiding walks crossing a square, arXiv:condmat/0506341, 2005.


FORMULA

x = sqrt(7/26 + sqrt(30261)/26).


EXAMPLE

x = 2.63815853034174086843...


MATHEMATICA

RealDigits[Sqrt[1/26*(7+Sqrt[30261])], 10, 120][[1]] (* Harvey P. Dale, Nov 22 2014 *)


PROG

(PARI) polrootsreal(13*x^47*x^2581)[2] \\ Charles R Greathouse IV, Apr 16 2014


CROSSREFS

Cf. A001411, A002931, A179260, A249776.
Sequence in context: A176014 A011447 A076041 * A021383 A296456 A256592
Adjacent sequences: A156813 A156814 A156815 * A156817 A156818 A156819


KEYWORD

cons,nonn


AUTHOR

Zak Seidov, Feb 16 2009


STATUS

approved



