A149418 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, 0), (-1, 1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 12, 55, 184, 879, 3283, 15929, 62222, 305006, 1233715, 6081876, 25181122, 124578183, 524939078, 2603359344, 11120535185, 55244397220, 238564600702, 1186615992619, 5170229157814, 25740573127296, 112994182925001, 562957176960359, 2486929397436891, 12397280542469366, 55065536289042493

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, 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, 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: A151478 A125528 A124005 * A149419 A367450 A151469

Adjacent sequences: A149415 A149416 A149417 * A149419 A149420 A149421

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved