A148700 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, 0, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 7, 23, 69, 241, 815, 2973, 10765, 40599, 153519, 594441, 2315819, 9159005, 36470431, 146745519, 594261517, 2425275509, 9954790549, 41110526691, 170626390065, 711716332495, 2981638200405, 12543716384153, 52971343747061, 224502013317731, 954637799193723, 4072108059395579

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, -1 + j, 1 + k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A148698 A148699 A181999 * A151268 A148701 A331685

Adjacent sequences: A148697 A148698 A148699 * A148701 A148702 A148703

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved