A149389 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, 0, 1), (-1, 1, 0), (1, -1, 0), (1, 0, -1), (1, 0, 1)}.

1, 1, 4, 12, 50, 177, 775, 3047, 13758, 57469, 264763, 1149410, 5370333, 23939506, 113009053, 513522505, 2443191002, 11263682171, 53918582307, 251379375951, 1209253867117, 5688175086909, 27472525104558, 130160859813314, 630734824597721, 3006067443247767, 14607506519085881, 69963210562397041

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 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: A151473 A152123 A149388 * A149390 A149391 A149392

Adjacent sequences: A149386 A149387 A149388 * A149390 A149391 A149392

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved