A148890 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, 0), (-1, 1, 0), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 8, 31, 99, 405, 1419, 5953, 22065, 96413, 370294, 1634168, 6465684, 28845552, 116211498, 525501390, 2151401160, 9780421638, 40586651280, 185562016495, 777580903830, 3577734848131, 15126428257970, 69843964271976, 297606647531008, 1378863798686027, 5911859813254132, 27491122663909053

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, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A360605 A119838 A148889 * A148891 A148892 A148893

Adjacent sequences: A148887 A148888 A148889 * A148891 A148892 A148893

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved