A149292 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), (-1, 1, 1), (1, -1, 0), (1, 1, 0)}.

1, 1, 4, 11, 46, 145, 641, 2287, 10362, 38721, 178975, 700051, 3274170, 13103091, 61899718, 253721395, 1206633562, 5014531143, 23988956031, 101185506495, 486117617820, 2069555088623, 9981081442588, 42926937379591, 207632770875770, 898992509896095, 4360150991226725, 19018904672979927

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, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + 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: A359707 A363663 A149291 * A149293 A149294 A149295

Adjacent sequences: A149289 A149290 A149291 * A149293 A149294 A149295

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved