A150295 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, 1, 0), (0, 1, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 6, 23, 95, 404, 1772, 7929, 36069, 166206, 773209, 3624790, 17102065, 81114678, 386455320, 1848256530, 8868663304, 42677840782, 205893327059, 995519646831, 4823016017342, 23407664566654, 113786451683742, 553923082837816, 2700082575328009, 13177194181392696, 64378824026712682, 314846186346791493

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A370285 A371827 A150294 * A150296 A134064 A111283

Adjacent sequences: A150292 A150293 A150294 * A150296 A150297 A150298

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved