A149477 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, 1), (-1, 1, 1), (0, 1, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 13, 57, 214, 979, 4092, 19118, 83810, 397074, 1792264, 8569134, 39449523, 189833114, 886149501, 4284798960, 20208047001, 98076614702, 466207454479, 2269386827433, 10854652323409, 52966000595103, 254608932972014, 1244890116366611, 6008783649970492, 29429687121612288, 142535485722942391

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[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A192372 A304670 A316117 * A149478 A149479 A149480

Adjacent sequences: A149474 A149475 A149476 * A149478 A149479 A149480

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved