A244088 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.

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, 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, 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

Offset: 1

Author

Jean-François Alcover, Jun 20 2014

Keywords

• nonn
• cons
• walk

Examples

			1.054700196225229122018341733456999376346353319...
		

References

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

Crossrefs

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

Programs

Mathematica

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

Formula

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