A149023 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, 1), (-1, 1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 9, 38, 129, 584, 2194, 10145, 40267, 189947, 778149, 3720871, 15595032, 75220900, 320698025, 1556317242, 6722501137, 32773080055, 143032577776, 699766105474, 3079695882812, 15108886597885, 66957520453531, 329225333017619, 1467564548391672, 7229091586888505, 32385804321356430

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, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A130407 A137031 A047148 * A149024 A149025 A351070

Adjacent sequences: A149020 A149021 A149022 * A149024 A149025 A149026

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved