A148718 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, 0, 1), (1, -1, -1), (1, 1, -1), (1, 1, 0)}.

1, 1, 3, 7, 24, 71, 268, 885, 3523, 12512, 51247, 191513, 800986, 3101457, 13187522, 52445940, 225832816, 917309222, 3989905040, 16483552983, 72298838407, 302864656959, 1337763501480, 5669506627016, 25192437651346, 107825554175631, 481602861028268, 2078839621541270, 9327122139005196

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A148715 A148716 A148717 * A003449 A258308 A148719

Adjacent sequences: A148715 A148716 A148717 * A148719 A148720 A148721

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved