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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, 0), (0, 1, -1), (1, 0, 1), (1, 1, -1), (1, 1, 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, 0), (0, 1, -1), (1, 0, 1), (1, 1, -1), (1, 1, 0)}
1, 2, 7, 25, 97, 390, 1611, 6794, 29091, 126090, 551977, 2436019, 10824817, 48383210, 217343673, 980622641, 4441459717, 20184954064, 92013044261, 420585882547, 1927209851761, 8850616244232, 40728874603093, 187776530443546, 867211015595651, 4011392950788858, 18582390286521855, 86198246458247689
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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[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