A149720 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, 1, 0), (1, -1, 1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 73, 295, 1347, 5829, 27169, 121841, 576633, 2652903, 12656631, 59103899, 284233127, 1342659713, 6487766429, 30900283921, 149947936161, 718950320529, 3499340747057, 16862097275321, 82299640491665, 398234447965951, 1947714354753959, 9456179522175335, 46335746276135371, 225604006948847023

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A149717 A149718 A149719 * A149721 A325156 A149722

Adjacent sequences: A149717 A149718 A149719 * A149721 A149722 A149723

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved