A149177 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, 0), (-1, 1, -1), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 10, 35, 124, 430, 1647, 6183, 23789, 93982, 369633, 1481709, 5983590, 24232012, 99222087, 407426130, 1680897964, 6975369570, 29010771057, 121164653294, 507700418550, 2132120381475, 8982067396981, 37920761022042, 160429930215705, 680251829388493, 2889238380694213, 12293506617026379

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A149175 A149176 A059710 * A149178 A344559 A318701

Adjacent sequences: A149174 A149175 A149176 * A149178 A149179 A149180

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved