A150111 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, 1, -1), (0, 1, -1), (1, 0, 0), (1, 0, 1)}.

1, 2, 6, 19, 70, 262, 1023, 4094, 16818, 69945, 294922, 1259081, 5426730, 23561608, 103046709, 453659247, 2007599774, 8925829461, 39864238925, 178747571197, 804199297973, 3629751750042, 16432391497625, 74589692974370, 339393460911899, 1547853224158976, 7074306420083226, 32394805350463378

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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[1 + i, -1 + j, 1 + 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: A150108 A150109 A150110 * A150112 A150113 A150114

Adjacent sequences: A150108 A150109 A150110 * A150112 A150113 A150114

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved