A150530 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, 1, -1), (0, 1, 1), (1, -1, 1), (1, 1, 0)}.

1, 2, 7, 25, 107, 436, 1988, 8626, 40383, 181774, 863053, 3976233, 19049695, 89148987, 429832065, 2033938473, 9853400726, 47009046208, 228573689009, 1097345190023, 5351235961000, 25817379702471, 126197005063640, 611264042341269, 2993732482130413, 14547976910603581, 71367049022673631

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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150528 A150529 A286761 * A150531 A150532 A074420

Adjacent sequences: A150527 A150528 A150529 * A150531 A150532 A150533

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved