A148949 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), (0, 1, -1), (1, 0, -1), (1, 1, 0)}.

1, 1, 3, 9, 30, 102, 395, 1494, 5954, 24246, 99891, 420520, 1789506, 7699288, 33491490, 146830382, 648682014, 2886460141, 12915080021, 58127021079, 262856872073, 1194064672913, 5446850836048, 24938556840756, 114584175869191, 528157899818023, 2441699192724964, 11319396207760376, 52610033400858505

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, j, 1 + k, -1 + n] + aux[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: A317875 A056333 A148948 * A148950 A148951 A228248

Adjacent sequences: A148946 A148947 A148948 * A148950 A148951 A148952

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved