A150746 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), (1, -1, 0), (1, 0, 1), (1, 1, 1)}

1, 2, 8, 29, 126, 524, 2387, 10508, 49101, 223021, 1057598, 4901311, 23459371, 110213887, 531005794, 2519326762, 12197210656, 58298225132, 283303981460, 1361870732353, 6637678026959, 32053652509631, 156602140421109, 759039843749156, 3715735770268940, 18064961431397008, 88580984939078797

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, -1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 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: A150743 A150744 A150745 * A150747 A150748 A150749

Adjacent sequences: A150743 A150744 A150745 * A150747 A150748 A150749

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved