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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

F. Faase, Counting Hamilton cycles in product graphs

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: A189499 A183159 A014345 * A149324 A149325 A149326

Adjacent sequences:  A006189 A006190 A006191 * A006193 A006194 A006195

KEYWORD

nonn,walk,nice,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified May 27 11:14 EDT 2017. Contains 287204 sequences.