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A025609
Number of n-move rook paths on 8 X 8 board from given corner to adjacent corner.
3
0, 1, 6, 64, 720, 9136, 122016, 1673344, 23216640, 323773696, 4525272576, 63308468224, 886046453760, 12403017773056, 173632453287936, 2430795572936704, 34030785382318080, 476428879520137216, 6669991618287108096, 93379806486052470784, 1307316833784928665600
OFFSET
0,3
COMMENTS
Paths are not required to be self-avoiding. - Andrew Howroyd, Nov 05 2019
FORMULA
G.f.: x*(1 - 12*x)/((1 + 2*x)*(1 - 6*x)*(1 - 14*x)).
a(n) = 18*a(n-1) - 44*a(n-2) - 168*a(n-3) for n >= 3.
MATHEMATICA
CoefficientList[ Series[(x - 12 x^2)/((1 + 2 x) (1 - 6 x) (1 - 14 x)), {x, 0, 16}], x]
PROG
(PARI) concat([0], Vec((1 - 12*x)/((1 + 2*x)*(1 - 6*x)*(1 - 14*x)) + O(x^20)))
CROSSREFS
Sequence in context: A237357 A230282 A186668 * A309186 A156887 A239847
KEYWORD
nonn,walk
EXTENSIONS
Terms a(17) and beyond from Andrew Howroyd, Nov 05 2019
STATUS
approved