A151189 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), (0, 0, -1), (0, 1, 1), (1, 0, 1), (1, 1, 0)}

1, 3, 12, 51, 232, 1068, 5038, 23959, 115138, 556622, 2705280, 13203258, 64641290, 317385682, 1561642298, 7698967867, 38015063016, 187965810828, 930489741852, 4610846698078, 22868608349166, 113508839545874, 563792941797046, 2802003291908282, 13933197934021940, 69316974046810338, 344994776781121974

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, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 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: A151187 A340893 A151188 * A199875 A064036 A195255

Adjacent sequences: A151186 A151187 A151188 * A151190 A151191 A151192

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved