A150733 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, 0, 0), (0, 0, 1), (1, 0, -1), (1, 1, 1)}.

1, 2, 8, 29, 122, 513, 2243, 9945, 44789, 203815, 936687, 4332665, 20183601, 94464361, 444300666, 2097754746, 9938925775, 47239005352, 225124194033, 1075566614995, 5150096298764, 24709433243624, 118774144300117, 571873440724543, 2757757069596343, 13317667222219943, 64397599612546547

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[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A220547 A261774 A345131 * A150734 A150735 A150736

Adjacent sequences: A150730 A150731 A150732 * A150734 A150735 A150736

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved