A150491 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, 0, 1), (0, 1, -1), (1, -1, 1), (1, 0, 0), (1, 0, 1)}.

1, 2, 7, 25, 100, 416, 1798, 7954, 35848, 163889, 757613, 3534070, 16606644, 78512097, 373082494, 1780537043, 8529153352, 40987209812, 197514653523, 954133743905, 4619062201883, 22404122173670, 108853541874327, 529689869626406, 2581069902609028, 12592741664790958, 61508342794636824, 300744674043060145

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, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A150488 A150489 A150490 * A346814 A178118 A150492

Adjacent sequences: A150488 A150489 A150490 * A150492 A150493 A150494

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved