A148765 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, -1, 0), (-1, 1, 1), (1, 0, -1), (1, 0, 1)}.

1, 1, 3, 7, 29, 89, 353, 1163, 5035, 18355, 77621, 287757, 1277101, 4987779, 21789935, 85442629, 385694431, 1563101755, 6967441627, 28231536045, 128944096445, 535005933021, 2416977305023, 10009791261227, 46100898374973, 194467533256391, 886898893115633, 3731434884743987, 17291364452077285

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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A096064 A148763 A148764 * A148766 A148767 A171180

Adjacent sequences: A148762 A148763 A148764 * A148766 A148767 A148768

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved