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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 (list; constant; graph; refs; listen; history; text; internal format)
 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

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Last modified September 8 13:51 EDT 2024. Contains 375753 sequences. (Running on oeis4.)