A148691 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), (-1, 1, 1), (0, 1, -1), (1, 0, 0)}.

1, 1, 3, 7, 23, 66, 225, 776, 2686, 9613, 35294, 131500, 487822, 1863370, 7150828, 27545304, 106963502, 420425777, 1654948705, 6538318841, 26054053228, 104186093986, 417521937748, 1680762430371, 6798820903048, 27542555089030, 111905074491059, 456321106093605, 1864989229835936

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, j, k, -1 + n] + aux[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, 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: A060089 A148689 A148690 * A148692 A201204 A106964

Adjacent sequences: A148688 A148689 A148690 * A148692 A148693 A148694

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved