A150349 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), (-1, 0, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 7, 23, 91, 338, 1413, 5574, 23971, 97986, 429233, 1797063, 7972403, 33958742, 152071651, 656286187, 2960241961, 12907599412, 58557022405, 257465167525, 1173532114075, 5195559106964, 23774554703729, 105870863607006, 486072384110133, 2175337722175658, 10015962384972937, 45018502131092791

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, 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: A150346 A150347 A150348 * A150350 A150351 A150352

Adjacent sequences: A150346 A150347 A150348 * A150350 A150351 A150352

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved