A149285 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), (1, -1, 1), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 11, 44, 158, 658, 2607, 11193, 46595, 204255, 875999, 3896188, 17047797, 76627162, 340148317, 1541155940, 6915715632, 31530564726, 142683439604, 653825245219, 2978569580564, 13705939356429, 62778713274257, 289894469530054, 1333800098361492, 6177646452734974, 28530308252975460

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, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + 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: A149283 A151436 A149284 * A149286 A149287 A149288

Adjacent sequences: A149282 A149283 A149284 * A149286 A149287 A149288

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved