A149163 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, 1), (1, -1, 0), (1, 1, 0)}

1, 1, 4, 9, 40, 119, 539, 1841, 8364, 30955, 141649, 549875, 2542866, 10164631, 47527100, 193802541, 914717352, 3788393117, 18005282017, 75561381227, 360910284426, 1531898228495, 7344956490924, 31475455042689, 151413448157436, 654028472348391, 3155668890434889, 13722284292332989

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[1 + i, -1 + j, -1 + 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: A149160 A149161 A149162 * A149164 A238420 A302179

Adjacent sequences: A149160 A149161 A149162 * A149164 A149165 A149166

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved