A149447 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, 1), (0, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 4, 13, 48, 178, 680, 2575, 10068, 38974, 152724, 599410, 2363912, 9311216, 36905368, 146022913, 579379360, 2300418218, 9145258964, 36352638418, 144764733828, 576290038860, 2296119072480, 9151959092974, 36493345883064, 145526722403676, 580706574965172, 2317133100092500

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[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A149444 A149445 A149446 * A357642 A149448 A149449

Adjacent sequences: A149444 A149445 A149446 * A149448 A149449 A149450

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved