A149842 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), (-1, 1, -1), (0, 1, 1), (1, 0, 0)}.

1, 2, 4, 12, 36, 110, 362, 1184, 3970, 13460, 46182, 160424, 558504, 1966559, 6952260, 24667781, 88039932, 315257113, 1132887337, 4082861443, 14761825714, 53495073036, 194274233075, 707197292768, 2579195023698, 9423152477327, 34484610652223, 126408613193178, 463988555923468, 1705361725173422

Offset

0,2

Links

Table of n, a(n) for n=0..29.

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, 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: A214936 A010552 A149841 * A149843 A226022 A272463

Adjacent sequences: A149839 A149840 A149841 * A149843 A149844 A149845

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved