A149741 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, -1, 1), (1, 1, 1)}

1, 1, 5, 17, 77, 313, 1461, 6377, 30137, 136451, 651723, 3016195, 14502915, 68098479, 329177579, 1561522961, 7577800745, 36219905503, 176326651911, 847707006233, 4137311253217, 19982038766867, 97730494112419, 473764845562387, 2321246109231415, 11287039830147797, 55385325458438225, 269998907629235517

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, -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: A149738 A149739 A149740 * A149742 A149743 A323794

Adjacent sequences: A149738 A149739 A149740 * A149742 A149743 A149744

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved