A149544 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, -1, 0), (-1, 1, 0), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 13, 55, 183, 797, 2857, 12825, 48217, 220507, 854979, 3952923, 15705777, 73027971, 295763237, 1381032123, 5676154103, 26604487189, 110624463481, 520256180685, 2183982552123, 10299802822029, 43589430230891, 206028701021297, 878062403228533, 4157818861743501, 17828220266161589

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, 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: A216821 A039510 A149543 * A149545 A149546 A149547

Adjacent sequences: A149541 A149542 A149543 * A149545 A149546 A149547

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved