A150231 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, 1), (0, -1, 1), (0, 0, 1), (1, 1, 0)}.

1, 2, 6, 22, 82, 322, 1298, 5350, 22426, 94916, 406746, 1757974, 7645144, 33472572, 147357332, 651595382, 2893278634, 12896473212, 57673136376, 258672021290, 1163439070392, 5245934689602, 23707011149574, 107363360719428, 487179080754400, 2214621379419896, 10084210450233258, 45990924044488522

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, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A360266 A360290 A191755 * A150232 A150233 A150234

Adjacent sequences: A150228 A150229 A150230 * A150232 A150233 A150234

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved