A148955 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, -1), (1, -1, 1), (1, 1, 0)}.

1, 1, 3, 9, 30, 104, 374, 1372, 5121, 19350, 73820, 283726, 1097104, 4262915, 16630036, 65090232, 255470039, 1005021759, 3961596740, 15642290396, 61853211838, 244889529931, 970627733761, 3850784072750, 15290025210880, 60755565168300, 241571260582169, 961066546034625, 3825451487035020

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + 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: A148953 A148954 A289602 * A119372 A145268 A148956

Adjacent sequences: A148952 A148953 A148954 * A148956 A148957 A148958

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved