A151036 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, 1, -1), (0, 0, 1), (0, 1, 0), (1, 0, 0)}.

1, 3, 9, 31, 117, 456, 1835, 7575, 31789, 135449, 584041, 2541918, 11157475, 49317508, 219300301, 980391826, 4403056567, 19856229162, 89874329340, 408123817360, 1858828844765, 8488904382060, 38861813105559, 178306374960843, 819783349514875, 3776166255112419, 17424518659217290, 80532473894255641

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, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A202180 A151034 A151035 * A073724 A375453 A151037

Adjacent sequences: A151033 A151034 A151035 * A151037 A151038 A151039

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved