A150731 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), (0, 1, -1), (0, 1, 1), (1, 0, -1), (1, 0, 1)}.

1, 2, 8, 28, 130, 532, 2528, 11232, 54018, 248164, 1212082, 5682304, 27893742, 133023140, 655148986, 3154342858, 15603065572, 75639961162, 374862248858, 1828672158604, 9074950870092, 44449162462130, 220966384291864, 1085680487597732, 5401935260776376, 26619308952466454, 132536670446683276

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[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: A075662 A150730 A307940 * A150732 A225689 A330211

Adjacent sequences: A150728 A150729 A150730 * A150732 A150733 A150734

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved