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%I #10 Jan 06 2020 20:33:08
%S 3,40,284,1912,13132,88608,577727,3659416,22719964,139088248,
%T 842307548,5055782456,30119691570,178296516264,1049685801023,
%U 6150604755800,35890214413836,208663068856540,1209212316951436,6987073893141896,40267076160162015,231512818498197668
%N Summed lengths of nonintersecting rook paths on a 4 X n board.
%C Paths are self-avoiding from one corner to the diagonally opposite corner.
%H Andrew Howroyd, <a href="/A181395/b181395.txt">Table of n, a(n) for n = 1..200</a>
%F Conjectured g.f.: x*(1 - x)*(3 - 29*x + 51*x^2 + 595*x^3 - 3879*x^4 + 9553*x^5 - 8366*x^6 - 8026*x^7 + 22931*x^8 - 13117*x^9 - 5593*x^10 + 7955*x^11 - 6118*x^12 + 6842*x^13 + 1884*x^14 - 6824*x^15 + 519*x^16 + 1991*x^17 - 206*x^18 - 230*x^19 + 13*x^20 + 9*x^21)/((1 - 8*x + 15*x^2 - 5*x^3 - 9*x^4 + 2*x^5 + x^6)^2*(1 - 4*x + 7*x^2 - 3*x^3 - 7*x^4 + 2*x^5 + x^6)^2). - _Andrew Howroyd_, Jan 06 2020
%Y Row 4 of A181399.
%Y Enumeration of these paths is A007786, related sequences A181394, A181396, A181397, A181398.
%K nonn
%O 1,1
%A _David Scambler_, Oct 17 2010
%E a(10)-a(13) from _Alois P. Heinz_, Dec 10 2011
%E Terms a(14) and beyond from _Andrew Howroyd_, Jan 06 2020
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