A149947 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), (0, 1, -1), (0, 1, 1), (1, 0, 0)}

1, 2, 5, 15, 50, 169, 598, 2164, 7854, 29048, 108552, 406591, 1537770, 5850165, 22293452, 85434661, 328608808, 1265532082, 4891237026, 18950820179, 73496281444, 285726717792, 1112723705763, 4336788466680, 16931361097317, 66186294616490, 258897318857957, 1013989918189022, 3975209368372994

Offset

0,2

Links

Table of n, a(n) for n=0..28.

Alin Bostan and Manuel Kauers, Automatic Classification of Restricted Lattice Walks, arXiv:0811.2899 [math.CO], 2008-2009.

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, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + 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: A149944 A149945 A149946 * A149948 A093129 A020876

Adjacent sequences: A149944 A149945 A149946 * A149948 A149949 A149950

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved