A149765 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), (-1, 1, 1), (0, -1, 0), (0, 1, -1), (1, 1, 1)}.

1, 1, 5, 19, 73, 299, 1267, 5449, 23695, 103995, 460999, 2057741, 9236055, 41657127, 188679191, 857797317, 3912417293, 17895491719, 82064705529, 377194431957, 1737324513829, 8017121194781, 37060041395185, 171586518757705, 795600298681499, 3693979078245015, 17172711550371335, 79926395247466553

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[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + 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: A129166 A149763 A149764 * A124464 A149766 A254686

Adjacent sequences: A149762 A149763 A149764 * A149766 A149767 A149768

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved