A148873 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, 1), (-1, 1, 1), (0, 1, -1), (1, 0, 1)}.

1, 1, 3, 8, 29, 97, 354, 1300, 5129, 19092, 77071, 302902, 1224459, 4889175, 20230479, 81922468, 339766702, 1398618423, 5853729563, 24226447913, 102042112312, 426606797100, 1802017383786, 7573988021017, 32177115099918, 135889802109788, 578695267283061, 2456508103944632, 10495089623826787

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A148870 A148871 A148872 * A148874 A022017 A148875

Adjacent sequences: A148870 A148871 A148872 * A148874 A148875 A148876

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved