A149166 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, 1, 0), (1, -1, 1), (1, 1, 0)}

1, 1, 4, 9, 42, 120, 570, 1825, 8890, 30534, 149418, 536896, 2650062, 9848282, 48696782, 185458037, 920584716, 3576385528, 17767869592, 70107220264, 348996559758, 1395354752334, 6949384790858, 28086919632832, 140041190373276, 571375438865004, 2849662081018354, 11720152721264588, 58492355525303946

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[1 + i, -1 + j, 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: A149165 A083859 A070761 * A149167 A149168 A149169

Adjacent sequences: A149163 A149164 A149165 * A149167 A149168 A149169

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved