A149769 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, 0, 1), (-1, 1, 0), (0, -1, 1), (0, 1, -1), (1, 1, 1)}.

1, 1, 5, 19, 75, 315, 1343, 5805, 25465, 112609, 501809, 2249753, 10137825, 45879657, 208411749, 949803899, 4341030175, 19891180107, 91353150651, 420421781995, 1938491735539, 8953427451639, 41419075782191, 191886308917751, 890170740176979, 4134728557660055, 19227740357351511, 89512590786210039

Offset

0,3

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, -1 + 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, k, -1 + n] + aux[1 + i, 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: A206373 A149767 A149768 * A149770 A285424 A275859

Adjacent sequences: A149766 A149767 A149768 * A149770 A149771 A149772

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved