A150311 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), (-1, 0, 1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 21, 86, 300, 1307, 4908, 22093, 86772, 398829, 1614603, 7528347, 31153064, 146762091, 617483907, 2931761937, 12497031704, 59698007965, 257166533447, 1234496848756, 5364413177604, 25854389616218, 113172524018212, 547266394015927, 2410533025207060, 11689387032359864, 51765982609024067

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[-1 + i, j, k, -1 + n] + aux[1 + 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: A150308 A150309 A150310 * A150312 A150313 A150314

Adjacent sequences: A150308 A150309 A150310 * A150312 A150313 A150314

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved