A149487 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), (-1, 1, 1), (1, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 13, 60, 241, 1152, 5047, 24522, 112283, 550476, 2585230, 12743808, 60807446, 300821244, 1450713881, 7194489294, 34955715150, 173659372472, 848372256917, 4220145869377, 20701409816068, 103077576284629, 507239684062705, 2527570853604017, 12469126050075458, 62170048090065723, 307313319397142302

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + 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: A115455 A241470 A219367 * A372125 A320359 A057712

Adjacent sequences: A149484 A149485 A149486 * A149488 A149489 A149490

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved