A149806 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, 1), (-1, 1, 1), (1, -1, 0), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 19, 91, 391, 1909, 8707, 42925, 201635, 999681, 4779393, 23770533, 114926985, 572668035, 2789841689, 13917541155, 68165695833, 340305135859, 1673296496661, 8357654984043, 41216239628539, 205929805755597, 1017860729611513, 5086671899646899, 25187014420646351, 125888798878141469

Offset

0,3

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, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A147139 A330445 A149805 * A149807 A149808 A371836

Adjacent sequences: A149803 A149804 A149805 * A149807 A149808 A149809

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved