A150838 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, 0, -1), (1, 1, 1)}.

1, 2, 8, 32, 137, 608, 2750, 12637, 58808, 275862, 1303674, 6196533, 29585580, 141832464, 682176597, 3290368486, 15910303667, 77097021916, 374301652563, 1820278278049, 8865480917493, 43236697516109, 211120315065097, 1032012445805406, 5049817660372877, 24732285539984953, 121232215049819753

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + k, -1 + n] + aux[-1 + i, 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: A150835 A150836 A150837 * A150839 A150840 A150841

Adjacent sequences: A150835 A150836 A150837 * A150839 A150840 A150841

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved