A149799 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, 0), (1, -1, 0), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 19, 87, 363, 1719, 7625, 36805, 169109, 824893, 3874641, 19020537, 90656173, 446915921, 2151851691, 10640076983, 51609398595, 255754672359, 1247387187887, 6191910245851, 30327782549171, 150739274838343, 740770047940151, 3685618022970599, 18160005964345643, 90426095901607687

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, 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: A147091 A149797 A149798 * A149800 A147099 A323788

Adjacent sequences: A149796 A149797 A149798 * A149800 A149801 A149802

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved