A149265 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, -1, -1), (-1, 0, 1), (-1, 1, 1), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 11, 40, 142, 540, 2009, 8017, 31012, 126096, 501651, 2065390, 8376028, 34811593, 143024546, 599037001, 2485562893, 10472855073, 43799101634, 185421645194, 780427538487, 3316944855477, 14032867218773, 59844292512609, 254259643037044, 1087478111800121, 4637070550057103

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A149264 A264331 A243760 * A149266 A149267 A149268

Adjacent sequences: A149262 A149263 A149264 * A149266 A149267 A149268

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved