login
A122680
Number of possible basketball games that end in a tie (n:n). Equivalently, the number of walks on the square lattice from (0,0) to (n,n) where the allowed steps are {(1,0),(2,0),(3,0), (0,1),(0,2),(0,3)}.
1
1, 2, 14, 106, 784, 6040, 47332, 375196, 3001966, 24190148, 196034522, 1596030740, 13044459766, 106961525744, 879512777006, 7249483605580, 59881171431050, 495545064567260, 4107666916668414, 34099685718629264, 283454909832384416, 2359069189033880228
OFFSET
0,2
LINKS
Moa Apagodu and Doron Zeilberger, FIVE Applications of Wilf-Zeilberger Theory to Enumeration and Probability; Local copy [Pdf file only, no active links]
M. Apagodu and D. Zeilberger, Maple package to generate recurrence; Local copy
M. Apagodu and D. Zeilberger, 6th order recurrence; Local copy
EXAMPLE
a(1) = 2 because the number of ways of getting the score to be (1,1) is
(0,0) -> (1,0) -> (1,1),
(0,0) -> (0,1) -> (1,1).
MAPLE
b:= proc(x, y) option remember; `if`(x<0 or y<0, 0,
`if`([x, y]=[0, 0], 1, add(b(x-i, y) +b(x, y-i), i=1..3)))
end:
a:= n-> b(n, n):
seq(a(n), n=0..30); # Alois P. Heinz, Jul 24 2011
MATHEMATICA
b[x_, y_] := b[x, y] = If[x < 0 || y < 0, 0, If[{x, y} == {0, 0}, 1, Sum[b[x - i, y] + b[x, y - i], {i, 3}]]];
a[n_] := b[n, n];
a /@ Range[0, 30] (* Jean-François Alcover, May 13 2020, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A343818 A160780 A279737 * A121122 A026293 A051708
KEYWORD
nonn,walk
AUTHOR
Doron Zeilberger, Oct 20 2006
STATUS
approved