A149029 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, 0), (0, 1, 1), (1, -1, 0), (1, 0, -1)}.

1, 1, 3, 10, 33, 118, 461, 1806, 7192, 29586, 123208, 519050, 2212177, 9504493, 41204497, 179859178, 789416425, 3484337220, 15452094569, 68819851405, 307696191256, 1380467355267, 6213170853187, 28045076820667, 126930546925837, 575886553389489, 2618708866944187, 11933055962219804

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A304824 A111639 A302076 * A149030 A024426 A326558

Adjacent sequences: A149026 A149027 A149028 * A149030 A149031 A149032

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved