A148064 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, -1, 1), (-1, 0, -1), (0, 1, 1), (1, -1, -1)}.

1, 1, 2, 3, 12, 25, 77, 201, 716, 1989, 6191, 20565, 67734, 215087, 713712, 2478469, 8338392, 27654245, 97731829, 339498647, 1168538528, 4069674521, 14553720972, 51368033395, 179774661926, 647707788441, 2325800861917, 8285237018781, 29798207595310, 108258428232621, 392093814282707, 1413452299369805

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[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, 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: A148061 A148062 A148063 * A148065 A148066 A148067

Adjacent sequences: A148061 A148062 A148063 * A148065 A148066 A148067

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved