A149001 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, -1, 1), (-1, 0, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 9, 34, 115, 468, 1742, 7367, 29009, 126186, 513867, 2277350, 9497955, 42648196, 181076473, 821244559, 3535010078, 16157583043, 70311352314, 323360554529, 1419681715996, 6561934763011, 29022457731324, 134705084724858, 599491925924524, 2792255475319458, 12492837790484781, 58362037794461010

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A148999 A149000 A160963 * A149002 A204446 A149003

Adjacent sequences: A148998 A148999 A149000 * A149002 A149003 A149004

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved