A149639 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), (0, 1, -1), (1, -1, 1), (1, 1, 1)}.

1, 1, 5, 15, 69, 261, 1189, 4997, 23011, 101409, 474129, 2142413, 10136447, 46598031, 222214471, 1035157901, 4963828023, 23358551315, 112507014881, 533522375907, 2579300250923, 12305507331249, 59674791214175, 286107311964209, 1391007954838179, 6696550282875709, 32627566832532271, 157617888654022555

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, -1 + k, -1 + n] + aux[i, -1 + 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: A149636 A149637 A149638 * A149640 A353173 A355603

Adjacent sequences: A149636 A149637 A149638 * A149640 A149641 A149642

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved