A150113 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), (-1, 1, -1), (1, 0, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 6, 19, 70, 262, 1032, 4112, 16957, 70398, 298251, 1270136, 5487853, 23805317, 104335318, 458787703, 2033142273, 9034828874, 40391226251, 181002360289, 814984158174, 3677166565567, 16655289870081, 75576045748501, 344027018703874, 1568580172677172, 7170851368252416, 32829693164473705

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + 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: A150110 A150111 A150112 * A150114 A199128 A150115

Adjacent sequences: A150110 A150111 A150112 * A150114 A150115 A150116

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved