A151014 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), (0, 1, -1), (1, -1, 1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 39, 182, 862, 4162, 20259, 99337, 489304, 2418609, 11984697, 59500280, 295825856, 1472439767, 7335264669, 36567210877, 182391230093, 910133114645, 4543159341619, 22684762319963, 113295004470674, 565938581524197, 2827451899485504, 14127870884837241, 70599917787569226, 352833539517667531

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + 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: A151011 A151012 A151013 * A151015 A151016 A151017

Adjacent sequences: A151011 A151012 A151013 * A151015 A151016 A151017

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved