A148080 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, 0, 1), (0, 1, -1), (1, 0, 0)}.

1, 1, 2, 4, 9, 24, 63, 199, 588, 1854, 6186, 19807, 67858, 232652, 807683, 2855387, 10155678, 36943753, 133283070, 490587798, 1824978741, 6745329088, 25387210981, 95888617570, 362818250454, 1383558309095, 5303541508493, 20420961071190, 78692710853813, 305683656774197, 1191240685138316, 4639998004350009

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[i, -1 + j, 1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A148078 A093156 A148079 * A148081 A148082 A148083

Adjacent sequences: A148077 A148078 A148079 * A148081 A148082 A148083

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved