A151252 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), (0, 1, 0), (1, 0, 0), (1, 1, 0), (1, 1, 1)}

1, 4, 18, 86, 414, 2026, 9962, 49220, 243940, 1211298, 6024982, 29999388, 149506288, 745566590, 3719918958, 18567624442, 92707299566, 463001495966, 2312799451962, 11554864879348, 57736384218564, 288523669037810, 1441956737106318, 7207007159715178, 36023360349838674, 180067567697351678

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, 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: A030278 A318217 A341248 * A084847 A082685 A111966

Adjacent sequences: A151249 A151250 A151251 * A151253 A151254 A151255

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved