A150797 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, 0), (0, -1, 0), (0, 1, -1), (0, 1, 1), (1, 0, 1)}

1, 2, 8, 31, 131, 569, 2555, 11578, 53466, 248535, 1167984, 5512501, 26206482, 124984773, 599074589, 2878285752, 13879661295, 67055935483, 324857576712, 1576140034786, 7663510420297, 37307124222965, 181925751178077, 888048200093199, 4340875408204790, 21236859873237790, 104014875002078419

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, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A150795 A027078 A150796 * A150798 A150799 A150800

Adjacent sequences: A150794 A150795 A150796 * A150798 A150799 A150800

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved