A149213 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, 1), (-1, 1, 0), (1, -1, 0), (1, 1, -1), (1, 1, 0)}.

1, 1, 4, 10, 42, 133, 583, 2107, 9498, 37100, 170422, 700327, 3260691, 13885192, 65303709, 285469307, 1353084601, 6034100741, 28777781725, 130354698204, 624801809350, 2865740094979, 13792513955173, 63908250241073, 308648304990584, 1442220043930524, 6985728178113346, 32873047087774126

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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A346889 A114918 A224488 * A149214 A149215 A149216

Adjacent sequences: A149210 A149211 A149212 * A149214 A149215 A149216

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved