A150077 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, 0, 1), (0, 1, -1), (1, 0, 0), (1, 1, 0)}.

1, 2, 6, 18, 66, 237, 910, 3560, 14383, 58323, 241477, 1013972, 4289049, 18269560, 78604459, 340648176, 1481407067, 6480432790, 28510899226, 125905971260, 557644102835, 2480504628972, 11071416464544, 49534764140683, 222208424115990, 999782628006911, 4508245709404073, 20367352284091797

Offset

0,2

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, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A037128 A150075 A150076 * A173385 A057693 A053496

Adjacent sequences: A150074 A150075 A150076 * A150078 A150079 A150080

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved