A148008 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, -1, 1), (-1, 0, 1), (-1, 1, -1), (1, 0, 0)}.

1, 1, 2, 3, 8, 15, 44, 91, 328, 759, 2636, 6215, 23704, 59033, 220830, 556591, 2236464, 5852471, 22914792, 60201671, 249117796, 672658877, 2717264406, 7345845087, 31036174078, 85697043495, 353999837354, 977097682671, 4193053543778, 11773887108191, 49467365565802, 138720176659439, 602452741040616

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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, j, k, -1 + n] + aux[1 + i, -1 + 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, 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: A151394 A148006 A148007 * A148009 A148010 A148011

Adjacent sequences: A148005 A148006 A148007 * A148009 A148010 A148011

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved