A150772 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, 1, -1), (1, 0, 1), (1, 1, 0)}

1, 2, 8, 30, 128, 555, 2481, 11293, 52078, 242765, 1140760, 5397133, 25670754, 122666597, 588385983, 2831555505, 13665200080, 66110756518, 320526990023, 1556979113295, 7575905400201, 36918299147880, 180151413324732, 880166375296829, 4305003235719407, 21077565141399016, 103292252810277194

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + 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: A150769 A150770 A150771 * A150773 A150774 A150775

Adjacent sequences: A150769 A150770 A150771 * A150773 A150774 A150775

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved