A149153 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, 0, 1), (-1, 1, -1), (1, -1, 0), (1, 1, 0)}.

1, 1, 4, 9, 38, 120, 514, 1787, 8042, 30024, 137224, 530796, 2480856, 9918516, 46702784, 190374471, 906997854, 3769136982, 18033009962, 75864970010, 365546041018, 1557303595620, 7524069805854, 32328005954926, 156919659652734, 680199365173406, 3307922174834418, 14428871521016760, 70397383520857038

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, -1 + j, k, -1 + 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[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}]

Crossrefs

Sequence in context: A149150 A149151 A149152 * A101529 A149154 A149155

Adjacent sequences: A149150 A149151 A149152 * A149154 A149155 A149156

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved