A150049 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, 0), (0, 0, 1), (0, 1, -1), (0, 1, 0), (1, 0, -1)}.

1, 2, 6, 18, 61, 214, 793, 2992, 11603, 45748, 183769, 746990, 3071538, 12748293, 53393963, 225310723, 957057631, 4089170129, 17567378065, 75844457539, 328890705035, 1431898090654, 6257271584888, 27438438709466, 120700011905225, 532496061724533, 2355605307331792, 10447128472323035

Offset

0,2

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, j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A393769 A150048 A363511 * A150050 A192318 A192483

Adjacent sequences: A150046 A150047 A150048 * A150050 A150051 A150052

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved