A148752 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, 0, -1), (1, 1, 0)}.

1, 1, 3, 7, 28, 77, 323, 1027, 4499, 15234, 68652, 244482, 1119699, 4128033, 19132050, 72551151, 339255496, 1313734573, 6186905395, 24392958836, 115515119719, 461965418939, 2197874309312, 8900519548172, 42506496184050, 173921532421315, 833329355690755, 3441435610292513, 16534808770189511

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, 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: A281701 A101303 A148751 * A148753 A148754 A148755

Adjacent sequences: A148749 A148750 A148751 * A148753 A148754 A148755

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved