A148031 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, 1), (-1, 0, 0), (0, -1, 1), (0, 1, 0), (1, -1, -1)}.

1, 1, 2, 3, 8, 17, 51, 124, 391, 1078, 3457, 10222, 33470, 105976, 352741, 1152698, 3894734, 13186214, 45455545, 156630035, 545896294, 1916833851, 6797318020, 24192288369, 86537326784, 311338858949, 1127841550001, 4103950196701, 14983432787528, 54911164910029, 202215706417259, 747845475495009, 2774088058155236

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + 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: A148028 A148029 A148030 * A148032 A148033 A148034

Adjacent sequences: A148028 A148029 A148030 * A148032 A148033 A148034

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved