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
AUTHOR
Jean-François Alcover, Jun 20 2014
STATUS
approved