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Search: id:A006192
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| A006192 |
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Number of nonintersecting (or self-avoiding) rook paths joining opposite corners of 3 X n board.
(Formerly M3453)
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4
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| 1, 4, 12, 38, 125, 414, 1369, 4522, 14934, 49322, 162899, 538020, 1776961, 5868904, 19383672, 64019918, 211443425, 698350194, 2306494009, 7617832222, 25159990674, 83097804242, 274453403399, 906458014440
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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H. L. Abbott and D. Hanson, A lattice path problem, Ars Combin., 6 (1978), 163-178.
S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 331-339.
Netnews group rec.puzzles, Frequently Asked Questions (FAQ) file. (Science Section).
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LINKS
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S. R. Finch, Self-Avoiding Walks of a Rook on a Chessboard
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FORMULA
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a(n) = 4a(n-1)-3a(n-2)+2a(n-3)+a(n-4) with a(0) = 0, a(1) = 1, a(2) = 4 and a(3) = 12. - Henry Bottomley (se16(AT)btinternet.com), Sep 05 2001
G.f.=x(1-x^2)/(1-4x+3x^2-2x^3-x^4). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 22 2004
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CROSSREFS
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Cf. A064297, A064298, A007786, A007787, A007764.
Sequence in context: A019480 A024590 A014345 this_sequence A122920 A009532 A056274
Adjacent sequences: A006189 A006190 A006191 this_sequence A006193 A006194 A006195
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KEYWORD
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nonn,walk,nice
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AUTHOR
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njas
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