A148144 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), (-1, 1, -1), (0, 1, -1), (1, 0, 0)}.

1, 1, 2, 4, 11, 29, 87, 279, 903, 2990, 10343, 36438, 129027, 468060, 1727245, 6402949, 24000526, 91225611, 348672208, 1339913947, 5198901440, 20295939931, 79512175548, 313402415099, 1242354896065, 4940265001927, 19721255437363, 79093149899843, 318190739681634, 1283561330395760, 5196080410244929

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[1 + i, -1 + j, 1 + 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: A317879 A148142 A148143 * A148145 A052869 A316768

Adjacent sequences: A148141 A148142 A148143 * A148145 A148146 A148147

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved