A148430 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, 1, 0), (0, 1, -1), (0, 1, 0), (1, -1, 1)}.

1, 1, 2, 5, 19, 59, 219, 774, 3145, 11859, 49307, 195291, 833909, 3407800, 14788168, 61947528, 272400290, 1162004530, 5161800599, 22345394684, 100082432241, 438344267322, 1976663086536, 8741628318605, 39643441874273, 176734752146518, 805373891611901, 3614987906351808, 16541733451593305

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, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A287019 A215169 A072468 * A062666 A148431 A321006

Adjacent sequences: A148427 A148428 A148429 * A148431 A148432 A148433

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved