A151171 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, 0), (1, 0, 0), (1, 1, 1)}

1, 3, 12, 49, 213, 949, 4315, 19948, 93051, 438391, 2076618, 9895800, 47347875, 227405295, 1095653934, 5292729849, 25629887924, 124354876370, 604493596562, 2943061130320, 14349482523619, 70053868908239, 342395885103390, 1675286128579784, 8204662187789668, 40217855422498911, 197298725918886144

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[i, -1 + j, 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: A049673 A052703 A151170 * A151172 A151173 A301456

Adjacent sequences: A151168 A151169 A151170 * A151172 A151173 A151174

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved