A151196 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), (0, 0, -1), (0, 1, 1), (1, 0, 1), (1, 1, 0)}

1, 3, 12, 52, 237, 1105, 5241, 25141, 121577, 591495, 2891010, 14180892, 69757821, 343937533, 1698947088, 8405296184, 41637856673, 206489110369, 1024962993224, 5091707834382, 25311342761319, 125899420245749, 626550433063709, 3119494357533251, 15537625064858015, 77417156971020527

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + 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: A268208 A007856 A151195 * A363090 A010736 A151197

Adjacent sequences: A151193 A151194 A151195 * A151197 A151198 A151199

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved