A150779 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, 0, 0), (1, 0, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 8, 30, 132, 551, 2514, 11092, 51627, 234627, 1105768, 5121388, 24346919, 114229926, 546518153, 2588237982, 12443907305, 59350043417, 286458618532, 1373763753193, 6651614457342, 32039257695971, 155538840748760, 751877996725337, 3658202605638155, 17736357156046623, 86459021455483368

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, j, 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: A150776 A150777 A150778 * A150780 A150781 A150782

Adjacent sequences: A150776 A150777 A150778 * A150780 A150781 A150782

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved