A148585 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, 0), (0, 0, -1), (1, 0, 0)}.

1, 1, 3, 6, 20, 54, 182, 578, 1994, 6876, 24510, 88314, 324753, 1204362, 4534353, 17203317, 65929875, 254661075, 990465401, 3878886425, 15278673944, 60503855579, 240843922447, 962901535611, 3866489329858, 15586583179789, 63056954545168, 255992060288283, 1042485185403142, 4257970164969914

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A148582 A148583 A148584 * A148586 A148587 A186409

Adjacent sequences: A148582 A148583 A148584 * A148586 A148587 A148588

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved