A148626 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, 0), (-1, 1, 0), (1, -1, -1), (1, 0, 1)}.

1, 1, 3, 6, 22, 54, 212, 601, 2431, 7371, 30743, 98770, 417771, 1390810, 5974821, 20539012, 88992084, 312709891, 1367861944, 4906398433, 21585896310, 78599131241, 348033315481, 1285612802379, 5716540037270, 21349908957726, 95376467758488, 360020793957497, 1613471261921915, 6141927630385251

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, j, 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: A079514 A148624 A148625 * A148627 A148628 A148629

Adjacent sequences: A148623 A148624 A148625 * A148627 A148628 A148629

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved