A148101 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), (0, 0, 1), (0, 1, -1), (1, -1, 0)}.

1, 1, 2, 4, 10, 26, 77, 231, 731, 2363, 7920, 27084, 94817, 336983, 1216568, 4453388, 16502271, 61814816, 233856348, 892573723, 3434288432, 13314937000, 51972107496, 204140373934, 806591451331, 3204158551284, 12792440649653, 51316797101243, 206757825981157, 836465018168185, 3397296971539772

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A149816 A149817 A149818 * A052854 A148102 A179381

Adjacent sequences: A148098 A148099 A148100 * A148102 A148103 A148104

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved