A151072 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), (0, 0, -1), (0, 1, 0), (0, 1, 1), (1, 0, 0)}.

1, 3, 10, 39, 163, 698, 3070, 13816, 63018, 290454, 1351773, 6339159, 29904498, 141807235, 675482905, 3229778815, 15493756268, 74541916820, 359542527108, 1738111831011, 8419375695658, 40856978894108, 198590179087079, 966691127754828, 4711921749598645, 22995200956892561, 112346622456221790

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 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: A253194 A367258 A338185 * A151073 A363555 A063688

Adjacent sequences: A151069 A151070 A151071 * A151073 A151074 A151075

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved