A149763 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, 0), (0, 1, -1), (1, 1, -1), (1, 1, 1)}

1, 1, 5, 19, 73, 297, 1253, 5393, 23441, 102615, 454053, 2024967, 9082141, 40939483, 185285179, 841711683, 3837192417, 17544665249, 80427480747, 369547466415, 1701549739581, 7850015140409, 36280336100217, 167946604147073, 778599094052733, 3614513361418427, 16801163253750261, 78189094551663749

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[i, 1 + j, 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: A255444 A287805 A129166 * A149764 A149765 A124464

Adjacent sequences: A149760 A149761 A149762 * A149764 A149765 A149766

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved