A149785 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, 0), (-1, 0, 1), (0, 1, -1), (1, -1, 1), (1, 1, 1)}.

1, 1, 5, 19, 81, 351, 1579, 7157, 33017, 153735, 721627, 3409687, 16198383, 77290035, 370247401, 1779351989, 8574843743, 41427163363, 200582985589, 973005897099, 4728070316299, 23010731777433, 112142523371387, 547204884943019, 2673195363475149, 13072644705328629, 63989169449142059, 313495876774479733

Offset

0,3

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, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A149783 A149784 A240688 * A149786 A149787 A323267

Adjacent sequences: A149782 A149783 A149784 * A149786 A149787 A149788

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved