A149795 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), (-1, 1, 1), (0, 1, -1), (1, -1, 1), (1, 1, 1)}.

1, 1, 5, 19, 85, 369, 1695, 7765, 36307, 170317, 807765, 3841717, 18383799, 88208733, 424946247, 2051518085, 9931383559, 48162942355, 234043500973, 1138948389163, 5551122811673, 27088130410373, 132345367637693, 647252376339615, 3168617573544485, 15525147860239259, 76130844445568163

Offset

0,3

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, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + 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: A149793 A282707 A149794 * A149796 A348410 A005191

Adjacent sequences: A149792 A149793 A149794 * A149796 A149797 A149798

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved