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 A006192 Number of nonintersecting (or self-avoiding) rook paths joining opposite corners of 3 X n board. (Formerly M3453) 7
 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; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES 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). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..150 H. L. Abbott and D. Hanson, A lattice path problem, Ars Combin., 6 (1978), 163-178. (Annotated scanned copy) F. Faase, Results from the counting program S. R. Finch, Self-Avoiding Walks of a Rook on a Chessboard Index entries for linear recurrences with constant coefficients, signature (4,-3,2,1). FORMULA 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, Sep 05 2001 G.f.=x(1-x^2)/(1-4x+3x^2-2x^3-x^4). - Emeric Deutsch, Dec 22 2004 MATHEMATICA LinearRecurrence[{4, -3, 2, 1}, {1, 4, 12, 38}, 40] (* Harvey P. Dale, Oct 05 2011 *) PROG (MAGMA) I:=[1, 4, 12, 38]; [n le 4 select I[n] else 4*Self(n-1)-3*Self(n-2)+2*Self(n-3)+Self(n-4): n in [1..30]]; // Vincenzo Librandi, Oct 06 2011 CROSSREFS Cf. A064297, A064298, A007786, A007787, A007764. Sequence in context: A183159 A289809 A014345 * A149324 A149325 A149326 Adjacent sequences:  A006189 A006190 A006191 * A006193 A006194 A006195 KEYWORD nonn,walk,nice,easy AUTHOR STATUS approved

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