A150660 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, 0, 1), (0, 1, 0), (1, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 28, 122, 553, 2571, 12160, 58208, 281102, 1366505, 6676481, 32747954, 161124710, 794716382, 3927618936, 19442645394, 96375419793, 478259944819, 2375582028014, 11809212355996, 58744206985928, 292388266077461, 1456030648082389, 7253832887596507, 36151517763970697, 180229899010820326

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, k, -1 + n] + aux[1 + i, 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: A352861 A293266 A150659 * A150661 A269228 A005435

Adjacent sequences: A150657 A150658 A150659 * A150661 A150662 A150663

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved