A148172 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, 1), (0, 1, -1), (1, 0, 1)}.

1, 1, 2, 4, 12, 27, 84, 224, 700, 1994, 6638, 19089, 64876, 198363, 664004, 2086517, 7239154, 22617762, 79274478, 257022722, 887577052, 2920427735, 10343306126, 33734494280, 120217932914, 402661589406, 1415512649780, 4785787121528, 17162415316492, 57471816051383, 206980298682640, 707863228732780

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, -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, 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: A219752 A242536 A027132 * A148173 A148174 A232218

Adjacent sequences: A148169 A148170 A148171 * A148173 A148174 A148175

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved