editing
approved
editing
approved
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, 0), (0, 1, 0), (1, 0, 0)}.
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, -1, 1), (-1, 0, 0), (0, 1, 0), (1, 0, 0)}
1, 2, 5, 15, 45, 143, 483, 1644, 5848, 21178, 77716, 290588, 1097869, 4182986, 16151078, 62672479, 245500460, 967557537, 3835676351, 15285272154, 61245921696, 246253276079, 995260779078, 4034182783045, 16419400425310, 67016453054374, 274452294823460, 1126645933307878, 4639258411263086
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, 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] + 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