A244088 - OEIS

%I #6 Jun 20 2014 03:40:05

%S 1,0,5,4,7,0,0,1,9,6,2,2,5,2,2,9,1,2,2,0,1,8,3,4,1,7,3,3,4,5,6,9,9,9,

%T 3,7,6,3,4,6,3,5,3,3,1,9,0,5,3,1,1,4,8,0,1,9,5,5,4,5,4,3,1,6,3,4,2,6,

%U 4,1,0,6,8,9,6,8,1,5,5,4,5,3,1,0,8,4,0,2,9,3,5,6,9,5,1,5,2,4,1,8

%N Decimal expansion of 1/2+2/sqrt(13), a constant related to the asymptotic evaluation of the number of self-avoiding rook paths joining opposite corners on a 3 X n chessboard.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.10.2 Rook paths on a chessboard, p. 334.

%F Asymptotic number of paths = p(k) ~ (1/2+2/sqrt(13)) * sqrt((3+sqrt(13))/2)^(2k), where k = n-1.

%e 1.054700196225229122018341733456999376346353319...

%t RealDigits[1/2 + 2/Sqrt[13], 10, 100] // First

%Y Cf. A006192, A007764, A007786, A007787, A244089.

%K nonn,cons,walk

%O 1,3

%A _Jean-François Alcover_, Jun 20 2014