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A244088
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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.
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1
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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
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OFFSET
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1,3
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.10.2 Rook paths on a chessboard, p. 334.
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LINKS
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FORMULA
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Asymptotic number of paths = p(k) ~ (1/2+2/sqrt(13)) * sqrt((3+sqrt(13))/2)^(2k), where k = n-1.
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EXAMPLE
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1.054700196225229122018341733456999376346353319...
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MATHEMATICA
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RealDigits[1/2 + 2/Sqrt[13], 10, 100] // First
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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