A148901 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, 0), (0, -1, 1), (0, 1, 0), (1, -1, 1), (1, 1, -1)}.

1, 1, 3, 8, 31, 111, 449, 1819, 7720, 33168, 145938, 649121, 2928423, 13329644, 61233113, 283276432, 1319087860, 6175891798, 29058459670, 137308405543, 651318916557, 3100055975387, 14800606807470, 70857861401493, 340081464183191, 1635921872887769, 7885698053327415, 38083566352583067

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A148898 A148899 A148900 * A148902 A213092 A352624

Adjacent sequences: A148898 A148899 A148900 * A148902 A148903 A148904

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved