A149167 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), (-1, 1, 1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 9, 42, 122, 590, 1909, 9352, 32288, 159348, 575336, 2852154, 10632642, 52848864, 201805251, 1004738946, 3909911352, 19488971892, 77013020910, 384181779814, 1537516796154, 7674311674350, 31042966872666, 155010703802680, 632789199449082, 3160749113086482, 13005667180995390

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, -1 + k, -1 + n] + aux[1 + 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: A083859 A070761 A149166 * A149168 A149169 A138544

Adjacent sequences: A149164 A149165 A149166 * A149168 A149169 A149170

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved