A148751 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, -1), (-1, -1, 1), (-1, 0, 1), (1, 0, -1), (1, 1, 0)}.

1, 1, 3, 7, 28, 77, 321, 1023, 4410, 15048, 66633, 238610, 1073045, 3988056, 18140939, 69296462, 318128048, 1241740863, 5741014612, 22809183833, 106052749451, 427559326268, 1997335409179, 8152169723075, 38232618177527, 157703344883955, 742071098595837, 3089039598322885, 14577060168438338

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, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A270349 A281701 A101303 * A148752 A148753 A148754

Adjacent sequences: A148748 A148749 A148750 * A148752 A148753 A148754

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved