A151160 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), (0, 1, 0), (1, 0, 0), (1, 1, -1), (1, 1, 1)}

1, 3, 11, 47, 211, 981, 4643, 22249, 107577, 523415, 2559557, 12562673, 61844559, 305170937, 1508729183, 7470679239, 37039545501, 183839555485, 913278679657, 4540455357403, 22588019286605, 112434351160019, 559923776128045, 2789586199714675, 13902995637729315, 69313036020027215, 345654829705408097

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, 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: A151158 A055731 A151159 * A151161 A227846 A124890

Adjacent sequences: A151157 A151158 A151159 * A151161 A151162 A151163

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved