A151153 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, 0), (0, 1, 0), (1, 0, 0), (1, 1, -1), (1, 1, 1)}

1, 3, 11, 47, 207, 937, 4315, 20131, 94791, 449385, 2143131, 10265971, 49358949, 238067903, 1151299263, 5580356587, 27101383325, 131848957507, 642427203243, 3134444254787, 15311819526033, 74880581522807, 366557824312123, 1796008273599715, 8807107180708079, 43220275188353973, 212248817015151835

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, 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: A151150 A151151 A151152 * A151154 A151155 A151156

Adjacent sequences: A151150 A151151 A151152 * A151154 A151155 A151156

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved