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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), (0, 1, -1), (1, 0, 0), (1, 1, 1)}.
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), (0, 1, -1), (1, 0, 0), (1, 1, 1)}
1, 2, 7, 25, 97, 404, 1693, 7388, 32505, 145180, 657113, 2989105, 13746349, 63477990, 294979025, 1377542831, 6455184517, 30385998096, 143414160901, 679093203299, 3224102213017, 15341517413850, 73177613623841, 349684935900806, 1674275884420683, 8029765418428754, 38569710367459915, 185545627362485953
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[-1 + i, j, k, -1 + n] + aux[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}]
nonn,walk
Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
approved