A148354 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, 0), (0, -1, 1), (0, 0, 1), (1, 1, -1)}.

1, 1, 2, 5, 15, 45, 141, 463, 1563, 5364, 18737, 66410, 238088, 861872, 3145644, 11564752, 42791022, 159184950, 595039609, 2234155149, 8420557767, 31846117947, 120823458983, 459696946312, 1753484378777, 6704441257002, 25689464721910, 98628288008785, 379353133321902, 1461549660613824, 5639706903125238

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A294502 A254534 A071727 * A364330 A151279 A149907

Adjacent sequences: A148351 A148352 A148353 * A148355 A148356 A148357

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved