A148054 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, 1, 1), (1, 0, 0)}.

1, 1, 2, 3, 10, 20, 68, 147, 530, 1224, 4408, 10516, 39378, 97474, 365038, 920535, 3501858, 9009592, 34248844, 89167304, 343038006, 905754654, 3484015834, 9277353140, 35924495108, 96578927300, 373891285428, 1011485913642, 3936897107170, 10729182442150, 41760445053660, 114370464498523, 446706120848602

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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, k, -1 + n] + aux[1 + 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: A148051 A148052 A148053 * A148055 A089791 A297872

Adjacent sequences: A148051 A148052 A148053 * A148055 A148056 A148057

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved