A149073 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, 0, 1), (-1, 1, 1), (0, 1, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 3, 11, 44, 183, 809, 3602, 16501, 76044, 355834, 1672025, 7928491, 37719595, 180484724, 865878172, 4170218920, 20127128889, 97409703571, 472252732792, 2294217886913, 11161310625475, 54384963658624, 265313713299804, 1295932502054133, 6336373253656207, 31012723918337793, 151918171332935560

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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

Crossrefs

Sequence in context: A122393 A012880 A200613 * A167011 A319322 A059714

Adjacent sequences: A149070 A149071 A149072 * A149074 A149075 A149076

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved