A151013 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), (0, 1, 1), (1, -1, 1), (1, 0, -1), (1, 1, 1)}.

1, 2, 9, 39, 182, 852, 4108, 19823, 96863, 473880, 2332888, 11496804, 56851680, 281377414, 1395432127, 6925190403, 34411294573, 171084261164, 851292169963, 4237755958166, 21107672581679, 105170417325035, 524231455105750, 2613788813959797, 13036097656965666, 65030749014857713, 324479983088294808

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[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: A151010 A151011 A151012 * A151014 A151015 A151016

Adjacent sequences: A151010 A151011 A151012 * A151014 A151015 A151016

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved