A150503 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), (0, 1, 1), (1, 1, 0)}.

1, 2, 7, 25, 102, 408, 1723, 7320, 31703, 138362, 611103, 2714012, 12133531, 54528943, 246177191, 1115631262, 5074220799, 23149462838, 105898900015, 485654339647, 2232247005041, 10281001178927, 47439927740353, 219279992251104, 1015163875320307, 4706592848028672, 21850761937459040, 101571656107705363

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[i, -1 + j, -1 + 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: A221455 A150501 A150502 * A150504 A150505 A150506

Adjacent sequences: A150500 A150501 A150502 * A150504 A150505 A150506

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved