A148464 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, 0, 0), (-1, 0, 1), (0, 0, -1), (0, 1, 0), (1, -1, 1)}.

1, 1, 2, 6, 19, 61, 209, 751, 2780, 10530, 40645, 159331, 634004, 2555818, 10406137, 42736003, 176987498, 738572161, 3101989207, 13102951031, 55643811842, 237474178387, 1018032832418, 4381947392234, 18932122549024, 82083627726775, 357053109955461, 1557819782212992, 6815800335178806

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[i, -1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A071646 A114627 A289591 * A148465 A148466 A094817

Adjacent sequences: A148461 A148462 A148463 * A148465 A148466 A148467

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved