A148892 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, 0, 1), (0, 1, 1), (1, -1, -1), (1, 1, -1)}.

1, 1, 3, 8, 31, 100, 421, 1552, 6762, 26907, 120089, 500608, 2276471, 9796176, 45167827, 198958096, 926982691, 4156792143, 19525807142, 88793214818, 419830105812, 1930734137846, 9178004031467, 42597152333828, 203400088951928, 951233632472524, 4559345764647379, 21459263407915619, 103190090318432504

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, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A148889 A148890 A148891 * A148893 A148894 A148895

Adjacent sequences: A148889 A148890 A148891 * A148893 A148894 A148895

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved