A148020 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), (0, 0, 1), (1, -1, 0), (1, 0, -1)}.

1, 1, 2, 3, 8, 17, 46, 127, 375, 1128, 3367, 10920, 34671, 112564, 378464, 1276401, 4367446, 15059481, 53064595, 187243903, 663669380, 2400056392, 8678448201, 31543452428, 115945737265, 428333746174, 1587547930666, 5915108954182, 22227724053667, 83642770868524, 315723019652527, 1201396034129496, 4579065456128057

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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[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: A148017 A148018 A148019 * A148021 A148022 A148023

Adjacent sequences: A148017 A148018 A148019 * A148021 A148022 A148023

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved