A150525 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, 0, -1), (0, 1, 1), (1, -1, 1), (1, 1, 0)}.

1, 2, 7, 25, 104, 428, 1881, 8234, 37201, 168388, 774534, 3576978, 16666951, 77997784, 366998557, 1733533658, 8218621913, 39089929073, 186433429979, 891484661419, 4272236389366, 20516796321394, 98708115461718, 475708444814502, 2296132506710913, 11098671038754329, 53717616206235570, 260306492054452636

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, 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, 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: A150522 A150523 A150524 * A150526 A150527 A150528

Adjacent sequences: A150522 A150523 A150524 * A150526 A150527 A150528

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved