A148652 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, 0, -1), (0, 1, 1), (1, -1, -1), (1, -1, 0)}.

1, 1, 3, 6, 24, 64, 225, 764, 2722, 9580, 35173, 131524, 490288, 1844811, 7149587, 27432934, 106212841, 417300569, 1642230108, 6477616246, 25747354409, 103049195615, 412277389692, 1656238693686, 6702816328113, 27121735507661, 110006258067148, 448644769198341, 1832242529748065

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, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A148649 A148650 A148651 * A148653 A148654 A148655

Adjacent sequences: A148649 A148650 A148651 * A148653 A148654 A148655

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved