A150992 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 1), (1, -1, 1), (1, 0, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 37, 171, 770, 3625, 16924, 80595, 382918, 1837819, 8819773, 42571079, 205627890, 996794721, 4836699211, 23525392935, 114539663040, 558627741653, 2727055503163, 13329987574645, 65212629715382, 319358257652623, 1565130485339104, 7676883257129551, 37679730531468542, 185068793084335583

Offset

0,2

Links

Table of n, a(n) for n=0..26.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, -1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A150989 A150990 A150991 * A151310 A000663 A364088

Adjacent sequences: A150989 A150990 A150991 * A150993 A150994 A150995

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved