A148068 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, -1), (-1, 1, 1), (1, 0, 0)}.

1, 1, 2, 3, 12, 25, 87, 189, 844, 2061, 8265, 20317, 94014, 246389, 1051736, 2752635, 12971752, 35409589, 156545721, 425681757, 2028643354, 5687451021, 25714495202, 71753924987, 344569097136, 984453928825, 4520756671327, 12852585508149, 62061211995954, 179832324062041, 835295154466845, 2408594166730577

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A148065 A148066 A148067 * A148069 A148070 A187994

Adjacent sequences: A148065 A148066 A148067 * A148069 A148070 A148071

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved