A150240 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, 1, 1), (1, -1, 0), (1, 0, 1)}.

1, 2, 6, 22, 83, 332, 1373, 5822, 25179, 110499, 491055, 2204416, 9982420, 45535322, 209028193, 964872868, 4475498448, 20848734247, 97495290610, 457494977005, 2153470741640, 10165210986423, 48107300289697, 228205944955031, 1084877223921258, 5167715978654237, 24661303067647016, 117889267175258159

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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + 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: A122449 A150238 A150239 * A150241 A150242 A150243

Adjacent sequences: A150237 A150238 A150239 * A150241 A150242 A150243

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved