A149964 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), (0, 0, 1), (1, 0, 0), (1, 1, -1)}.

1, 2, 5, 16, 54, 191, 722, 2789, 11005, 44606, 183005, 760686, 3204874, 13610213, 58310598, 251807779, 1093664345, 4779427288, 20995536151, 92637168280, 410555645864, 1826337575865, 8152470233379, 36511687311687, 163990870698843, 738588127619303, 3334949540166910, 15092994027753804

Offset

0,2

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, k, -1 + n] + aux[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: A141754 A149962 A149963 * A148399 A149965 A149966

Adjacent sequences: A149961 A149962 A149963 * A149965 A149966 A149967

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved