A148357 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, 0, 0), (0, 0, 1), (1, -1, -1), (1, 1, -1)}.

1, 1, 2, 5, 15, 45, 150, 500, 1768, 6449, 23952, 90754, 350352, 1366671, 5412378, 21657356, 87478719, 356678716, 1465294690, 6061674645, 25247400391, 105746887056, 445393747063, 1885309697875, 8016785181291, 34236548716423, 146792552622838, 631691350559110, 2727914538208874

Offset

0,3

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A149909 A149910 A149911 * A149912 A148358 A149913

Adjacent sequences: A148354 A148355 A148356 * A148358 A148359 A148360

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved