A150477 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, -1), (0, 0, 1), (1, -1, 0), (1, 1, 1)}.

1, 2, 7, 25, 99, 408, 1743, 7592, 33719, 151442, 687913, 3151179, 14538075, 67481244, 314877361, 1475843667, 6945055325, 32796434702, 155356830111, 737985256349, 3514444677653, 16774687944748, 80233031911899, 384480428069964, 1845654312853857, 8874050298857830, 42730272114282057, 206036821996122797

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, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150474 A150475 A150476 * A333249 A151537 A074421

Adjacent sequences: A150474 A150475 A150476 * A150478 A150479 A150480

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved