A149596 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), (-1, 0, -1), (1, -1, 0), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 15, 59, 219, 943, 3751, 15899, 67527, 294375, 1259641, 5562709, 24487903, 108724571, 481848287, 2168462967, 9716498853, 43820690213, 197919279247, 899976839611, 4082879396573, 18626354550873, 85052300771561, 389645946518697, 1784418455640275, 8205115564469679, 37737886034050155

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, j, 1 + 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: A230986 A149594 A149595 * A149597 A149598 A149599

Adjacent sequences: A149593 A149594 A149595 * A149597 A149598 A149599

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved