A149497 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, 0, -1), (1, -1, -1), (1, 1, 1)}.

1, 1, 5, 9, 45, 109, 497, 1505, 6277, 21933, 87881, 327701, 1317185, 5003189, 20502937, 78367049, 325943661, 1259386365, 5266016649, 20655292081, 86435272421, 343588605953, 1439975562709, 5775301253901, 24286476447881, 97980723577541, 413563223119177, 1677143349827301, 7098191690374505

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[1 + i, 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: A145031 A121724 A149496 * A149498 A149499 A100305

Adjacent sequences: A149494 A149495 A149496 * A149498 A149499 A149500

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved