A148800 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, 0, 1), (0, 0, -1), (0, 1, 1), (1, -1, 0)}

1, 1, 3, 8, 25, 86, 294, 1040, 3833, 14386, 54712, 210824, 822979, 3247027, 12924638, 51841966, 209371068, 851006530, 3478406410, 14290345910, 58982156747, 244473647740, 1017286372274, 4248218090559, 17800061935502, 74813151306454, 315342569996696, 1332772451282701, 5647021916205779

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[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 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: A006372 A148798 A148799 * A244278 A190343 A185043

Adjacent sequences: A148797 A148798 A148799 * A148801 A148802 A148803

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved