A149834 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), (0, 1, -1), (0, 1, 0), (1, 0, -1), (1, 0, 0)}.

1, 2, 4, 10, 30, 94, 316, 1112, 3976, 14798, 56508, 217444, 856594, 3430942, 13813620, 56463442, 233440548, 968955348, 4064389254, 17189382700, 72928723582, 311804852012, 1341392988174, 5785742781494, 25102210579594, 109434792302328, 478132786545494, 2098665310659574, 9247115836091400

Offset

0,2

Links

Table of n, a(n) for n=0..28.

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, j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[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: A148116 A149833 A026119 * A273958 A362637 A149835

Adjacent sequences: A149831 A149832 A149833 * A149835 A149836 A149837

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved