A151086 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, 0, 1), (0, 1, 0), (1, 0, 0), (1, 1, 0)}

1, 3, 11, 41, 163, 678, 2908, 12689, 56096, 251383, 1139337, 5208786, 23965775, 110924342, 516254394, 2414349496, 11335791596, 53407506243, 252434493264, 1196694418646, 5687965950378, 27098001229588, 129372363727450, 618882875806662, 2965990345592723, 14238142354747679, 68454394635253561

Offset

0,2

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, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A084077 A339037 A027103 * A151087 A149066 A149067

Adjacent sequences: A151083 A151084 A151085 * A151087 A151088 A151089

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved