A148844 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), (0, 1, -1), (1, 0, 0)}.

1, 1, 3, 8, 27, 96, 361, 1409, 5650, 23184, 96687, 409555, 1754124, 7592661, 33139803, 145727381, 644928721, 2870241308, 12837405152, 57669438763, 260088377628, 1177136924040, 5344629210546, 24336621999021, 111107986827919, 508478801070057, 2332153406603864, 10718196697490856, 49351328396155123

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, j, k, -1 + n] + aux[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: A148843 A340334 A319787 * A145760 A102318 A102206

Adjacent sequences: A148841 A148842 A148843 * A148845 A148846 A148847

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved