A151239 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, 0), (0, 0, 1), (1, 0, -1), (1, 0, 1), (1, 1, 1)}.

1, 3, 14, 64, 307, 1485, 7269, 35755, 176665, 875277, 4345792, 21609460, 107578587, 536028717, 2672677318, 13333233492, 66543700069, 332218051799, 1659035211312, 8286699157204, 41398391047875, 206846040896581, 1033621721279993, 5165563569986093, 25817143778058803, 129040837679109879

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A101476 A060801 A292744 * A151240 A161131 A247978

Adjacent sequences: A151236 A151237 A151238 * A151240 A151241 A151242

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved