A149435 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, 0, 1), (0, 1, -1), (1, -1, 0), (1, 1, 1)}.

1, 1, 4, 13, 46, 166, 616, 2317, 8818, 33862, 130906, 508690, 1985158, 7773886, 30528118, 120165583, 473939962, 1872379006, 7407691624, 29343102082, 116356441630, 461821527304, 1834453407664, 7291975192036, 29003636757940, 115424203565524, 459569872509772, 1830597853159408

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, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A180144 A149434 A026641 * A149436 A087440 A149437

Adjacent sequences: A149432 A149433 A149434 * A149436 A149437 A149438

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved