A150324 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, 0), (1, 0, -1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 22, 86, 316, 1314, 5236, 22608, 94591, 418720, 1809437, 8152191, 36042798, 164532212, 739869381, 3411910087, 15543863248, 72262806914, 332620036343, 1556574199804, 7224695770488, 33995656854255, 158873726063244, 751049396267312, 3530122036974346, 16754410594433543, 79134147930815117

Offset

0,2

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, j, 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: A014558 A150322 A150323 * A150325 A102311 A150326

Adjacent sequences: A150321 A150322 A150323 * A150325 A150326 A150327

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved