A149679 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, 0), (1, 0, -1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 67, 247, 1099, 4455, 19545, 81193, 367927, 1586737, 7157861, 31187449, 142977035, 635088717, 2905801469, 12983274605, 59979785943, 271113149209, 1251408664667, 5678125929285, 26377652274927, 120606171091533, 560085080932585, 2567797002056437, 11979145771661855, 55218140871183393

Offset

0,3

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A153323 A059847 A149678 * A149680 A149681 A149682

Adjacent sequences: A149676 A149677 A149678 * A149680 A149681 A149682

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved