A148445 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), (-1, 0, 1), (0, 1, 1), (1, 0, -1)}.

1, 1, 2, 6, 17, 49, 170, 563, 1932, 7030, 25301, 93316, 352510, 1328907, 5104863, 19787771, 76973523, 303046762, 1198411018, 4763383468, 19074052627, 76619234449, 309290295334, 1254304906918, 5101316718791, 20831445235339, 85334661234543, 350503839679277, 1444195911346241, 5964913563214104

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[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A122099 A026165 A336742 * A148446 A244401 A244402

Adjacent sequences: A148442 A148443 A148444 * A148446 A148447 A148448

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved