A148398 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), (0, 1, -1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 5, 16, 53, 201, 751, 2969, 11912, 48722, 202963, 857651, 3662901, 15846173, 69089287, 303942174, 1346846163, 6005971987, 26944569704, 121509650966, 550564330442, 2505673556481, 11448107083346, 52497934562648, 241548938785273, 1114836139179427, 5160272351336388, 23949236821028822

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, 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A148396 A108521 A148397 * A346518 A100442 A081126

Adjacent sequences: A148395 A148396 A148397 * A148399 A148400 A148401

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved