A149348 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, 0, 0), (0, -1, 1), (0, 1, -1), (1, -1, 0), (1, 1, 0)}.

1, 1, 4, 12, 42, 153, 593, 2333, 9522, 39283, 165815, 706828, 3058009, 13331249, 58754207, 260519211, 1164703413, 5233155799, 23664405546, 107456289612, 490466225257, 2246496796421, 10333356366661, 47673400810091, 220721796088564, 1024559018474286, 4770112516366437, 22258699966303098

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, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A149346 A149347 A173411 * A149349 A149350 A149351

Adjacent sequences: A149345 A149346 A149347 * A149349 A149350 A149351

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved