A149130 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, 0, 1), (1, -1, 0), (1, 1, 0)}.

1, 1, 4, 9, 34, 105, 401, 1367, 5476, 19349, 80273, 292215, 1232272, 4620353, 19623528, 75369853, 321847302, 1257747177, 5400963549, 21375561605, 92259387954, 368913498877, 1598656123316, 6449996890877, 28034718346216, 113997014502371, 496687111946723, 2033213200131901, 8877506245499802

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, 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: A163069 A149128 A149129 * A149131 A149132 A149133

Adjacent sequences: A149127 A149128 A149129 * A149131 A149132 A149133

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved