A149847 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), (-1, -1, 0), (-1, -1, 1), (0, 1, 0), (1, 0, 1)}.

1, 2, 4, 14, 46, 134, 502, 1820, 5980, 23198, 87922, 306836, 1216060, 4729934, 17121082, 68851202, 272448226, 1010816594, 4108318162, 16458898196, 62164300252, 254714419202, 1030026465334, 3943455360182, 16261959193558, 66245444855966, 256342162541710, 1062615874236728, 4354486276936816

Offset

0,2

Links

Table of n, a(n) for n=0..28.

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[i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A014272 A070822 A101536 * A149848 A149849 A149850

Adjacent sequences: A149844 A149845 A149846 * A149848 A149849 A149850

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved