A150693 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, 1), (-1, 1, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 8, 26, 118, 438, 2078, 8209, 39754, 162831, 797320, 3344263, 16483408, 70313101, 348008609, 1503387856, 7461490857, 32553374801, 161874095473, 711874224388, 3544621282571, 15690913376927, 78205701748159, 348111360116639, 1736283725383760, 7765241828198106, 38751745866315018, 174023171833791778

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, -1 + j, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A150690 A150691 A150692 * A150694 A150695 A150696

Adjacent sequences: A150690 A150691 A150692 * A150694 A150695 A150696

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved