A149454 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, 0), (-1, 1, 1), (0, -1, 1), (1, 0, -1), (1, 1, 0)}

1, 1, 4, 13, 49, 198, 822, 3529, 15479, 69033, 311992, 1426666, 6580201, 30587772, 143122551, 673348718, 3183437184, 15113727614, 72019102558, 344308018891, 1650844243543, 7935833965393, 38237726668241, 184631028260387, 893191083199476, 4328485864367581, 21009390791266280, 102121755567680032

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, -1 + j, k, -1 + 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, 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: A149452 A140660 A149453 * A101125 A284336 A230081

Adjacent sequences: A149451 A149452 A149453 * A149455 A149456 A149457

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved