A149748 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, 0, 1), (0, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 79, 327, 1487, 6677, 30717, 142149, 664989, 3122187, 14783737, 70121443, 334613209, 1599628705, 7675931117, 36908653065, 177910757393, 859149747059, 4156876166657, 20141966655907, 97752117263755, 474977703967981, 2310931985472255, 11255214218375295, 54876297938703683, 267802180953226221

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, 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: A149745 A149746 A149747 * A151494 A307052 A369262

Adjacent sequences: A149745 A149746 A149747 * A149749 A149750 A149751

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved