A149958 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), (0, 1, 0), (1, 0, -1), (1, 0, 0)}

1, 2, 5, 16, 53, 190, 712, 2748, 10955, 44472, 184169, 774033, 3294304, 14186277, 61653079, 270328574, 1194121104, 5310366701, 23760820194, 106886302347, 483240427871, 2194532068235, 10007208426762, 45807047821678, 210404752046038, 969585995010804, 4481347901048146, 20770094033642776

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[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 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: A268430 A047006 A127498 * A148395 A148396 A108521

Adjacent sequences: A149955 A149956 A149957 * A149959 A149960 A149961

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved