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A244089
Decimal expansion of sqrt((3+sqrt(13))/2), a constant related to the asymptotic evaluation of the number of self-avoiding rook paths joining opposite corners on a 3 X n chessboard.
1
1, 8, 1, 7, 3, 5, 4, 0, 2, 1, 0, 2, 3, 9, 7, 0, 6, 2, 0, 0, 7, 5, 1, 9, 4, 4, 8, 6, 0, 3, 5, 8, 2, 1, 9, 2, 6, 4, 6, 9, 4, 0, 3, 6, 4, 3, 1, 2, 7, 1, 3, 6, 1, 1, 2, 0, 6, 3, 3, 0, 7, 7, 0, 5, 8, 2, 7, 9, 8, 9, 9, 4, 3, 8, 6, 8, 3, 6, 5, 6, 9, 3, 6, 7, 8, 1, 9, 2, 0, 1, 7, 8, 1, 0, 0, 6, 2, 6, 7, 8
OFFSET
1,2
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.10.2 Rook paths on a chessboard, p. 334.
FORMULA
Asymptotic number of paths = p(k) ~ (1/2+2/sqrt(13)) * sqrt((3+sqrt(13))/2)^(2k), where k = n-1.
EXAMPLE
1.8173540210239706200751944860358219264694...
MATHEMATICA
RealDigits[Sqrt[(3 + Sqrt[13])/2], 10, 100] // First
CROSSREFS
KEYWORD
nonn,cons,walk
AUTHOR
STATUS
approved