cp's OEIS Frontend

A006192 Number of nonintersecting (or self-avoiding) rook paths joining opposite corners of 3 X n board.

%I A006192 M3453 #45 Sep 08 2022 08:44:34
%S A006192 1,4,12,38,125,414,1369,4522,14934,49322,162899,538020,1776961,
%T A006192 5868904,19383672,64019918,211443425,698350194,2306494009,7617832222,
%U A006192 25159990674,83097804242,274453403399,906458014440
%N A006192 Number of nonintersecting (or self-avoiding) rook paths joining opposite corners of 3 X n board.
%D A006192 H. L. Abbott and D. Hanson, A lattice path problem, Ars Combin., 6 (1978), 163-178.
%D A006192 S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 331-339.
%D A006192 Netnews group rec.puzzles, Frequently Asked Questions (FAQ) file. (Science Section).
%D A006192 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006192 Vincenzo Librandi, <a href="/A006192/b006192.txt">Table of n, a(n) for n = 1..150</a>
%H A006192 H. L. Abbott and D. Hanson, <a href="/A006189/a006189.pdf">A lattice path problem</a>, Ars Combin., 6 (1978), 163-178. (Annotated scanned copy)
%H A006192 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a>
%H A006192 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A006192 Steven R. Finch, <a href="/FinchGammel.html">Self-Avoiding Walks of a Rook on a Chessboard</a> [From Steven Finch, Apr 20 2019]
%H A006192 Steven R. Finch, <a href="/FinchFlajolet.html">Self-Avoiding Walks of a Rook</a> [From Steven Finch, Apr 20 2019; mentioned in Finch's "Gammel" link above]
%H A006192 Steven R. Finch, <a href="/FinchMarxen.html">Table of Non-Overlapping Rook Paths</a> [From Steven Finch, Apr 20 2019; mentioned in Finch's "Gammel" link above]
%H A006192 D. G. Radcliffe, N. J. A. Sloane, C. Cole, J. Gillogly, & D. Dodson, <a href="/A007765/a007765.pdf">Emails, 1994</a>
%H A006192 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,2,1).
%F A006192 a(n) = 4*a(n-1) - 3*a(n-2) + 2*a(n-3) + a(n-4) with a(0) = 0, a(1) = 1, a(2) = 4 and a(3) = 12. - _Henry Bottomley_, Sep 05 2001
%F A006192 G.f.: x*(1-x^2)/(1 - 4*x + 3*x^2 - 2*x^3 - x^4). - _Emeric Deutsch_, Dec 22 2004
%t A006192 LinearRecurrence[{4,-3,2,1},{1,4,12,38},40] (* _Harvey P. Dale_, Oct 05 2011 *)
%o A006192 (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
%Y A006192 Cf. A064297, A064298, A007786, A007787, A007764.
%K A006192 nonn,walk,nice,easy
%O A006192 1,2
%A A006192 _N. J. A. Sloane_