A150487 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, 1, 1), (0, 0, 1), (1, 0, -1), (1, 1, 0)}.

1, 2, 7, 25, 100, 412, 1770, 7757, 34715, 157340, 721929, 3340801, 15582566, 73129582, 345078964, 1635861836, 7785924688, 37188831495, 178173911708, 856008810970, 4122545235871, 19898003323666, 96229368799540, 466210250864806, 2262351350838510, 10994593882046659, 53503978995352478, 260693768734287260

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150484 A150485 A150486 * A150488 A150489 A150490

Adjacent sequences: A150484 A150485 A150486 * A150488 A150489 A150490

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved