A150775 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, 1, 0), (0, 0, -1), (1, 0, 0), (1, 1, 1)}

1, 2, 8, 30, 130, 560, 2515, 11414, 52747, 245438, 1153428, 5451143, 25915808, 123731198, 593089167, 2852055352, 13755006246, 66500899299, 322217412195, 1564256873782, 7607081045206, 37050749287155, 180708563205005, 882479863916443, 4314455261165435, 21115325837211025, 103438362436377391

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[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A150772 A150773 A150774 * A150776 A150777 A150778

Adjacent sequences: A150772 A150773 A150774 * A150776 A150777 A150778

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved