A150352 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, 0, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 7, 23, 91, 341, 1430, 5698, 24704, 102022, 451844, 1910457, 8586273, 36916061, 167694462, 730079744, 3343399996, 14698697009, 67740524161, 300152425534, 1390342199532, 6200291804167, 28840604723911, 129311967245448, 603591153468590, 2718773161204798, 12727897213195416, 57558443741744198

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, -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, 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: A150349 A150350 A150351 * A150353 A150354 A150355

Adjacent sequences: A150349 A150350 A150351 * A150353 A150354 A150355

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved