A149263 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, 0), (-1, 0, 1), (1, 0, -1), (1, 1, 1)}.

1, 1, 4, 11, 40, 128, 484, 1641, 6334, 22270, 86616, 312454, 1220466, 4479292, 17560954, 65232393, 256488726, 961512650, 3788566998, 14305980766, 56457883232, 214441375622, 847362995744, 3233911640424, 12792266119044, 49015447106540, 194058705431670, 746071256677748, 2955972696302066

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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A149260 A149261 A149262 * A149264 A264331 A243760

Adjacent sequences: A149260 A149261 A149262 * A149264 A149265 A149266

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved