A148493 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, 0), (0, 0, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 2, 6, 21, 81, 330, 1378, 5931, 26103, 116949, 531180, 2439942, 11308763, 52813717, 248226279, 1173038179, 5569350953, 26549412251, 127009530189, 609483954875, 2932752862535, 14146308968347, 68383627370230, 331211588348031, 1607013923709855, 7809477167061254, 38005744065563414

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, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A150210 A148492 A150211 * A148494 A150212 A150213

Adjacent sequences: A148490 A148491 A148492 * A148494 A148495 A148496

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved