A151141 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, 1), (0, 1, -1), (0, 1, 1), (1, 0, 0), (1, 0, 1)}

1, 3, 11, 46, 207, 941, 4415, 21045, 100678, 486957, 2370954, 11563058, 56680194, 278759272, 1372238073, 6773424153, 33496331672, 165743991475, 821426350054, 4075614613481, 20229562090050, 100510570736767, 499753226502617, 2485527626416439, 12369880809903471, 61592426685346230, 306744102770414629

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A198413 A151140 A271959 * A275757 A291090 A155134

Adjacent sequences: A151138 A151139 A151140 * A151142 A151143 A151144

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved