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%I #28 Feb 07 2024 09:36:36
%S 1,8,38,184,976,5382,29739,163496,896476,4913258,26932712,147657866,
%T 809563548,4438573234,24335048679,133419610132,731487691902,
%U 4010463268476,21987818897998,120550710615560,660932932108467
%N Number of nonintersecting rook paths joining opposite corners of 4 X n board.
%D Netnews group rec.puzzles, Frequently Asked Questions (FAQ) file. (Science Section).
%H Harvey P. Dale, <a href="/A007786/b007786.txt">Table of n, a(n) for n = 1..1000</a>
%H F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a>
%H F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H F. Faase, <a href="http://www.iwriteiam.nl/Crook_path.html">Rook path problem</a>
%H D. G. Radcliffe, N. J. A. Sloane, C. Cole, J. Gillogly, & D. Dodson, <a href="/A007765/a007765.pdf">Emails, 1994</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-54,124,-133,-16,175,-94,-69,40,12,-4,-1).
%F a(n) = 12*a(n - 1) - 54*a(n - 2) + 124*a(n - 3) - 133*a(n - 4) - 16*a(n - 5) + 175*a(n - 6) - 94*a(n - 7) - 69*a(n - 8) + 40*a(n - 9) + 12*a(n - 10) - 4*a(n - 11) - a(n - 12). - _Vladeta Jovovic_, Mar 20 2000
%F G.f.: x*(x^10-15*x^8+6*x^7+50*x^6-26*x^5-39*x^4+36*x^3-4*x^2-4*x+1) / ((x^6+2*x^5-9*x^4-5*x^3+15*x^2-8*x+1)*(x^6+2*x^5-7*x^4-3*x^3+7*x^2-4*x+1)). [_Colin Barker_, Nov 24 2012]
%t LinearRecurrence[{12,-54,124,-133,-16,175,-94,-69,40,12,-4,-1},{1,8,38,184,976,5382,29739,163496,896476,4913258,26932712,147657866},30] (* _Harvey P. Dale_, Jun 27 2012 *)
%Y Row 4 of A064298.
%Y Cf. A006192, A007764, A007787.
%K nonn,easy,nice,walk
%O 1,2
%A Heiner Marxen
%E More terms from _Vladeta Jovovic_, Mar 20 2000