A148033 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, 1), (-1, 1, -1), (0, -1, 1), (1, 0, 0)}.

1, 1, 2, 3, 8, 17, 51, 131, 421, 1207, 3878, 12057, 40118, 130680, 441485, 1497749, 5185040, 17987644, 63307623, 224664807, 803719579, 2891171202, 10485345696, 38262391388, 140319647872, 517205785586, 1916799857203, 7134782171482, 26659616659966, 100023181578858, 376737643518470, 1423639450605206

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, j, 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] + 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: A148030 A148031 A148032 * A148034 A148035 A148036

Adjacent sequences: A148030 A148031 A148032 * A148034 A148035 A148036

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved