A150341 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, 0, -1), (0, -1, 0), (1, 0, 1), (1, 1, 0)}.

1, 2, 7, 23, 89, 334, 1361, 5438, 22865, 94784, 407045, 1728913, 7538835, 32581158, 143720183, 629266387, 2801110393, 12389597024, 55557069245, 247746634259, 1117689957727, 5017645126782, 22752329266419, 102716654869034, 467793906696163, 2121978774344404, 9700314055341291, 44183124548096243

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.

J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]

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, j, -1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A150340 A339038 A001338 * A150342 A124190 A176578

Adjacent sequences: A150338 A150339 A150340 * A150342 A150343 A150344

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved