A148656 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, -1), (0, 1, 1), (1, -1, -1), (1, 1, -1)}

1, 1, 3, 6, 24, 64, 234, 773, 2834, 9831, 37010, 136510, 515786, 1945824, 7551398, 28998957, 113230854, 443548687, 1754250827, 6920531600, 27637345567, 110388869744, 443391403250, 1783214166259, 7222153140203, 29236895471647, 118939528499130, 484637762074954, 1982394583968022

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, 1 + j, 1 + 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, 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: A148653 A148654 A148655 * A279300 A054718 A132390

Adjacent sequences: A148653 A148654 A148655 * A148657 A148658 A148659

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved