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%I #17 Feb 13 2023 15:07:24
%S 1,0,14,84,896,10080,127904,1708224,23426816,325032960,4532831744,
%T 63353816064,886318555136,12404650352640,173642248822784,
%U 2430854346031104,34031138021113856,476430995352453120,6670004313281921024,93379882656019513344,1307317290804734590976
%N Number of n-move rook paths on 8 X 8 board from given corner to same corner.
%C Paths are not required to be self-avoiding. - _Andrew Howroyd_, Nov 05 2019
%H Andrew Howroyd, <a href="/A025607/b025607.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (18,-44,-168).
%F G.f.: (1 - 18*x + 58*x^2)/((1 + 2*x)*(1 - 6*x)*(1 - 14*x)).
%F a(n) = 18*a(n-1) - 44*a(n-2) - 168*a(n-3) for n >= 3. - _Andrew Howroyd_, Nov 05 2019
%t CoefficientList[ Series[(1 - 18 x + 58 x^2)/((1 + 2 x) (1 - 6 x) (1 - 14 x)), {x, 0, 16}], x]
%t LinearRecurrence[{18,-44,-168},{1,0,14},30] (* _Harvey P. Dale_, Feb 13 2023 *)
%o (PARI) Vec((1 - 18*x + 58*x^2)/((1 + 2*x)*(1 - 6*x)*(1 - 14*x)) + O(x^20)) \\ _Andrew Howroyd_, Nov 05 2019
%Y Cf. A025608, A025609.
%K nonn,easy,walk
%O 0,3
%A _David W. Wilson_
%E Terms a(17) and beyond from _Andrew Howroyd_, Nov 05 2019
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