A150900 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), (0, 1, 1), (1, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 8, 34, 158, 740, 3580, 17356, 85288, 419548, 2076994, 10289214, 51136938, 254268828, 1266516436, 6310682704, 31475418234, 157026615060, 783840256578, 3913440650712, 19545339350726, 97629965409706, 487774051594668, 2437217363303416, 12179542157773952, 60869055430440472, 304230022508786944

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[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: A368763 A150898 A150899 * A084207 A151305 A150901

Adjacent sequences: A150897 A150898 A150899 * A150901 A150902 A150903

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved