The OEIS is supported by the many generous donors to the OEIS Foundation.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #16 Nov 06 2019 01:11:10
%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