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_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, 0), (-1, -1, 1), (0, 0, 1), (0, 1, 0), (1, 1, -1)}
1, 2, 5, 15, 50, 176, 646, 2452, 9549, 37961, 153511, 629732, 2614885, 10972374, 46463260, 198334111, 852639288, 3688754625, 16049389276, 70187680379, 308375520541, 1360617913209, 6026613738270, 26788857783196, 119469665596501, 534412213485831, 2397257900073820, 10781700156879226
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, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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