A148335 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, 1), (0, 1, 0), (1, -1, 1), (1, 0, -1)}.

1, 1, 2, 5, 14, 44, 144, 487, 1690, 5968, 21410, 77778, 285486, 1057276, 3944582, 14810725, 55915246, 212094912, 807838800, 3088078508, 11842326972, 45542436464, 175586377976, 678496358882, 2627165030106, 10191179906996, 39599018198800, 154099574168302, 600506786025438, 2343056952632564

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A137557 A306799 A369590 * A268419 A149883 A307786

Adjacent sequences: A148332 A148333 A148334 * A148336 A148337 A148338

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved