login
A148171
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, 0, 1), (-1, 1, 1), (0, -1, 1), (0, 1, 0), (1, 0, -1)}.
0
1, 1, 2, 4, 11, 32, 106, 356, 1276, 4657, 17645, 68100, 269090, 1079751, 4402729, 18173798, 75897938, 320069369, 1361833054, 5839681294, 25218300840, 109593862795, 479006422233, 2104508479189, 9289937873731, 41186208290004, 183320357570998, 818938861833152, 3670712111578903
OFFSET
0,3
LINKS
A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
MATHEMATICA
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, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
CROSSREFS
Sequence in context: A156043 A268322 A375641 * A318644 A113774 A124504
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved