|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Paths are not required to be self-avoiding. - Andrew Howroyd, Nov 05 2019
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn,walk
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|