A149789 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), (-1, 1, 1), (0, 1, -1), (1, -1, 0), (1, 1, 1)}.

1, 1, 5, 19, 83, 359, 1621, 7397, 34287, 160329, 756171, 3587343, 17109611, 81943397, 393873557, 1898913021, 9178998447, 44469765073, 215871925197, 1049749029221, 5112681871005, 24935204015019, 121763599883763, 595264154554159, 2913026575292897, 14268630331252561, 69950213039800301

Offset

0,3

Links

Table of n, a(n) for n=0..26.

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, -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: A340736 A094726 A149788 * A149790 A017963 A149791

Adjacent sequences: A149786 A149787 A149788 * A149790 A149791 A149792

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved