A149469 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, 0, 1), (-1, 1, 1), (0, 1, -1), (1, -1, 0), (1, 1, 0)}.

1, 1, 4, 13, 54, 214, 919, 3984, 17772, 80080, 366595, 1691770, 7877604, 36926470, 174112034, 824899323, 3925561729, 18748361538, 89833469739, 431690857897, 2079682186282, 10041508850305, 48584193517259, 235491620594297, 1143330270479493, 5559375459322033, 27068814795311369, 131963539891053946

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, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A145208 A149467 A149468 * A229182 A149470 A149471

Adjacent sequences: A149466 A149467 A149468 * A149470 A149471 A149472

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved