A149047 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, 0), (1, 1, -1)}.

1, 1, 3, 10, 38, 142, 588, 2437, 10461, 45436, 201286, 901394, 4075139, 18588924, 85449323, 395126467, 1837179948, 8584943255, 40290867700, 189791115778, 897095411261, 4253625142255, 20224200143286, 96397912640423, 460545684750707, 2204930841748683, 10576608120323346, 50823903382293844

Offset

0,3

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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, 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: A078109 A149045 A149046 * A196469 A083692 A308124

Adjacent sequences: A149044 A149045 A149046 * A149048 A149049 A149050

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved