A150160 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, 0), (0, 1, -1), (0, 1, 1), (1, 0, 0)}.

1, 2, 6, 20, 75, 281, 1140, 4553, 19070, 79211, 339345, 1443963, 6293297, 27237166, 120173370, 526927586, 2346463311, 10393195395, 46629996570, 208201003414, 939887637241, 4224266435704, 19167503541672, 86623568278189, 394759085127664, 1792395700857280, 8198828862514061, 37376552890612858

Offset

0,2

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, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A318402 A293492 A150159 * A150161 A150162 A150163

Adjacent sequences: A150157 A150158 A150159 * A150161 A150162 A150163

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved