A148972 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, 0, -1), (0, 1, 1), (1, -1, 0), (1, 1, -1)}.

1, 1, 3, 9, 32, 106, 426, 1630, 6384, 25946, 108308, 445189, 1877503, 8022260, 34370984, 148012675, 643610626, 2817324764, 12368693445, 54448245375, 241561372630, 1075228964553, 4787473330615, 21431052382410, 96316712546439, 433054378646430, 1952963046254572, 8836449646395901, 40041198913314657

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A034538 A034540 A148971 * A148973 A148974 A148975

Adjacent sequences: A148969 A148970 A148971 * A148973 A148974 A148975

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved