A151127 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, 1), (0, 1, 0), (1, 0, 1), (1, 1, 0)}.

1, 3, 11, 45, 195, 863, 3918, 18099, 84257, 396308, 1877474, 8934493, 42733799, 205223131, 988269150, 4773483124, 23114429524, 112134123653, 545063420222, 2653927027638, 12939274069976, 63172294283413, 308793205348011, 1510922614233746, 7400378954267824, 36279213666808984, 177990698037930169

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, j, -1 + 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: A151124 A151125 A151126 * A026375 A151128 A049183

Adjacent sequences: A151124 A151125 A151126 * A151128 A151129 A151130

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved