A149449 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), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 13, 48, 186, 754, 3101, 13081, 55918, 241842, 1056729, 4653512, 20636905, 92045421, 412664764, 1858189426, 8400280703, 38106109901, 173399399510, 791243931982, 3619695024654, 16597056340441, 76261008077190, 351083803055512, 1619160434708842, 7479651981112689, 34604569511020325

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[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: A149447 A357642 A149448 * A149450 A297591 A294298

Adjacent sequences: A149446 A149447 A149448 * A149450 A149451 A149452

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved