A148658 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, 1, -1), (-1, 1, 0), (1, -1, -1), (1, 0, 1)}

1, 1, 3, 6, 25, 65, 263, 818, 3460, 11295, 49589, 171337, 756364, 2728977, 12218413, 45154693, 204526668, 774395008, 3523749667, 13608411568, 62334220137, 244098295369, 1124429301897, 4462694940662, 20623721325354, 82801756928869, 384104350127336, 1556170558698583, 7243115019135401

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, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A144227 A174473 A148657 * A148659 A148660 A148661

Adjacent sequences: A148655 A148656 A148657 * A148659 A148660 A148661

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved