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, 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.

Links

Table of n, a(n) for n=1..100.

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

Cf. A006192, A007764, A007786, A007787, A244088.

Sequence in context: A182551 A005486 A010157 * A195489 A245280 A200585

Adjacent sequences: A244086 A244087 A244088 * A244090 A244091 A244092

Keyword

nonn,cons,walk

Author

Jean-François Alcover, Jun 20 2014

Status

approved