reviewed

approved

proposed

reviewed

editing

proposed

A. Alin Bostan and M. Manuel Kauers, 2008<a href="http://arxiv.org/abs/0811. 2899">Automatic Classification of Restricted Lattice Walks, </a href="http>, arXiv://arxiv.org/abs/0811.2899">ArXiv 0811 [math.2899</a>CO], 2008-2009.

approved

editing

_Manuel Kauers (manuel(AT)kauers.de), _, Nov 18 2008

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, 0, 0), (0, 1, 0), (0, 1, 1), (1, 0, -1)}

1, 2, 5, 15, 50, 175, 643, 2442, 9497, 37772, 152757, 626466, 2602060, 10918685, 46235865, 197396778, 848640258, 3671712505, 15976961310, 69874586990, 307024031593, 1354759662530, 6001007238525, 26676880710809, 118977537295689, 532239704904251, 2387650011379440, 10739032580822009

0,2

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, <a href="http://arxiv.org/abs/0811.2899">ArXiv 0811.2899</a>.

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, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, j, 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}]

nonn,walk

Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008

approved