A149873 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, 0), (-1, 1, -1), (0, 0, 1), (0, 1, 1), (1, -1, -1)}.

1, 2, 5, 13, 42, 138, 491, 1734, 6592, 24830, 96763, 378378, 1522997, 6125484, 24995807, 102864877, 427821311, 1785014345, 7503833522, 31780141158, 135203016714, 577262116273, 2478171737927, 10689904205292, 46240610852179, 200652119456436, 874430567808585, 3821828494391071, 16740354639430228

Offset

0,2

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, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A149870 A149871 A149872 * A149874 A114297 A178682

Adjacent sequences: A149870 A149871 A149872 * A149874 A149875 A149876

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved