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A025609 Number of n-move rook paths on 8 X 8 board from given corner to adjacent corner. 3

%I

%S 0,1,6,64,720,9136,122016,1673344,23216640,323773696,4525272576,

%T 63308468224,886046453760,12403017773056,173632453287936,

%U 2430795572936704,34030785382318080,476428879520137216,6669991618287108096,93379806486052470784,1307316833784928665600

%N Number of n-move rook paths on 8 X 8 board from given corner to adjacent corner.

%C Paths are not required to be self-avoiding. - _Andrew Howroyd_, Nov 05 2019

%H Andrew Howroyd, <a href="/A025609/b025609.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.: x*(1 - 12*x)/((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.

%t CoefficientList[ Series[(x - 12 x^2)/((1 + 2 x) (1 - 6 x) (1 - 14 x)), {x, 0, 16}], x]

%o (PARI) concat([0], Vec((1 - 12*x)/((1 + 2*x)*(1 - 6*x)*(1 - 14*x)) + O(x^20)))

%Y Cf. A025607, A025608.

%K nonn,walk

%O 0,3

%A _David W. Wilson_

%E Terms a(17) and beyond from _Andrew Howroyd_, Nov 05 2019

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Last modified October 3 06:40 EDT 2022. Contains 357231 sequences. (Running on oeis4.)