A149378 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, 0), (-1, 0, 1), (0, 0, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 12, 48, 172, 704, 2832, 12048, 51167, 222291, 972073, 4314357, 19287153, 86967804, 394239816, 1798586922, 8247848422, 38011507458, 175879906285, 816790596799, 3806042455632, 17792597421918, 83419217824454, 392122329044956, 1847566010330373, 8724681867410249, 41287279746464866

Offset

0,3

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, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A149376 A149377 A063887 * A149379 A149380 A149381

Adjacent sequences: A149375 A149376 A149377 * A149379 A149380 A149381

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved