A148253 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, 0), (0, 1, -1), (1, -1, 1), (1, 0, 0)}.

1, 1, 2, 4, 13, 38, 133, 472, 1765, 6824, 27021, 109776, 454221, 1910817, 8155244, 35228927, 153824125, 678070366, 3013894753, 13496603167, 60844279321, 275940416256, 1258264355646, 5765883287937, 26540341660458, 122667242961872, 569091334275080, 2649328455973642, 12372953219581326

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, j, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A148252 A268698 A174604 * A148254 A163137 A093630

Adjacent sequences: A148250 A148251 A148252 * A148254 A148255 A148256

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved