A150485 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, 0, 1), (0, 0, 1), (1, 0, -1), (1, 1, 0)}.

1, 2, 7, 25, 100, 411, 1762, 7684, 34263, 154390, 705455, 3245690, 15075629, 70363983, 330663437, 1559532714, 7392718601, 35142810992, 167708548701, 802144487018, 3848350875625, 18496839933707, 89121639137457, 430066464149684, 2079486130381680, 10067919094667254, 48825121101713796, 237043776743413260

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, 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: A150482 A150483 A150484 * A150486 A150487 A150488

Adjacent sequences: A150482 A150483 A150484 * A150486 A150487 A150488

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved