A149112 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, -1), (1, -1, 0), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 8, 36, 100, 464, 1468, 6965, 23905, 114844, 416216, 2016743, 7602555, 37059549, 143921898, 704672428, 2801020997, 13760655759, 55729821081, 274505700986, 1128929959934, 5572377477788, 23212875492651, 114773157528287, 483343556780482, 2393175485857705, 10173033731720672, 50428380890679632

Offset

0,3

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A149110 A354735 A149111 * A221842 A100214 A229535

Adjacent sequences: A149109 A149110 A149111 * A149113 A149114 A149115

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved