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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

M. Apagodu and D. Zeilberger, FIVE Applications of WZ Theory to Enumeration and Probability

M. Apagodu and D. Zeilberger, Maple package to generate recurrence

M. Apagodu and D. Zeilberger, 6th order recurrence

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

CROSSREFS

Sequence in context: A293044 A160780 A279737 * A121122 A026293 A051708

Adjacent sequences:  A122677 A122678 A122679 * A122681 A122682 A122683

KEYWORD

nonn,walk

AUTHOR

Doron Zeilberger, Oct 20 2006

STATUS

approved

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Last modified November 19 06:03 EST 2019. Contains 329310 sequences. (Running on oeis4.)