A149413 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), (-1, 1, 0), (1, 0, 1), (1, 1, -1)}

1, 1, 4, 12, 53, 177, 828, 3092, 14784, 57789, 280272, 1135447, 5552568, 23024141, 113220356, 477899480, 2359089266, 10094151186, 49965552101, 216128476308, 1071992173208, 4678195921440, 23239176677578, 102166556126257, 508113249104213, 2247796432093211, 11189390004754332, 49765229004840975

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, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A190342 A262745 A180381 * A149414 A053454 A149415

Adjacent sequences: A149410 A149411 A149412 * A149414 A149415 A149416

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved