A150036 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), (0, 1, -1), (1, 0, 1)}.

1, 2, 6, 17, 63, 222, 868, 3265, 13405, 53275, 223259, 914164, 3909764, 16388698, 70927944, 302334626, 1322634824, 5711521875, 25182959651, 109885961160, 487770976428, 2146224129991, 9579356119447, 42445372186746, 190338310464854, 848302510691958, 3819433753111438, 17107621720377267

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, -1 + k, -1 + n] + aux[i, -1 + 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, 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: A347825 A150035 A000661 * A150037 A150038 A150039

Adjacent sequences: A150033 A150034 A150035 * A150037 A150038 A150039

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved