A150066 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, 0, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 6, 18, 64, 214, 778, 2720, 10190, 36714, 138694, 508120, 1942400, 7215578, 27705234, 103824766, 401157256, 1515305878, 5870905470, 22296702332, 86720976072, 331044670238, 1289979296838, 4942444807358, 19309656528546, 74248791281038, 290477529192398, 1119911259584580, 4389615790395500

Offset

0,2

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[1 + 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: A150064 A148463 A150065 * A150067 A150068 A150069

Adjacent sequences: A150063 A150064 A150065 * A150067 A150068 A150069

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved