A148222 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, -1, -1)}.

1, 1, 2, 4, 13, 31, 94, 288, 946, 2917, 10331, 34045, 120115, 415549, 1512332, 5302702, 19776363, 71123552, 267102964, 981067962, 3733058123, 13858243095, 53413593289, 200752884416, 778834373500, 2963095481252, 11576603104622, 44393765834319, 174808116767733, 675300877166206, 2673209809473755

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, -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: A148219 A148220 A148221 * A148223 A148224 A148225

Adjacent sequences: A148219 A148220 A148221 * A148223 A148224 A148225

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved