A150187 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), (0, 1, -1), (0, 1, 1), (1, 0, 0)}.

1, 2, 6, 21, 74, 283, 1118, 4474, 18418, 76926, 324603, 1386443, 5975585, 25934455, 113306676, 498104688, 2200289474, 9762376912, 43502560144, 194545972756, 872853253320, 3928480242241, 17730045779203, 80220588463158, 363827774353128, 1653728798863828, 7531862909604940, 34368356466413236

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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[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: A116738 A360151 A150186 * A116818 A294770 A116763

Adjacent sequences: A150184 A150185 A150186 * A150188 A150189 A150190

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved