A150055 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, 0), (0, 0, -1), (0, 0, 1), (1, 0, 0)}.

1, 2, 6, 18, 62, 217, 818, 3121, 12381, 49571, 203049, 839400, 3521390, 14897035, 63638310, 273791526, 1186143557, 5169379953, 22649963428, 99731867420, 441044844823, 1958337923511, 8726940635121, 39020752850638, 175010536790968, 787164676052659, 3549874609418846, 16047893490021657

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, j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A150053 A150054 A067052 * A150056 A204686 A098964

Adjacent sequences: A150052 A150053 A150054 * A150056 A150057 A150058

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved