A150059 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, 0), (0, 0, 1), (0, 1, -1), (1, 0, 0)}.

1, 2, 6, 18, 63, 220, 835, 3154, 12570, 49819, 205075, 839526, 3536313, 14817881, 63500843, 270794862, 1176087811, 5084586904, 22320018345, 97564133595, 432038519652, 1905633255140, 8500244263894, 37776633883543, 169546296602137, 758326978376323, 3421466506580925, 15387354919855504

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, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A079469 A150057 A150058 * A150060 A150061 A150062

Adjacent sequences: A150056 A150057 A150058 * A150060 A150061 A150062

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved