A148000 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, 0, 1), (1, 0, -1)}.

1, 1, 2, 3, 8, 15, 39, 87, 254, 633, 1755, 4817, 13683, 38328, 109188, 327645, 962488, 2855001, 8585783, 26100683, 79038683, 239634748, 749702378, 2323224093, 7216147407, 22570101754, 71214487008, 224091470121, 704212414119, 2258037023357, 7208557781173, 23017651439589, 73774471716580

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..160

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Maple

b:= proc(n, l) option remember; `if`(-1 in {l[]}, 0, `if`(n=0, 1,
      add(b(n-1, l+d), d=[[-1, -1, 0], [-1, 1, -1],
                          [0, 0, 1], [1, 0, -1]])))
    end:
a:= n-> b(n, [0$3]):
seq (a(n), n=0..40);  # Alois P. Heinz, Feb 19 2013

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, j, 1 + k, -1 + n] + aux[i, 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: A049957 A151255 A147999 * A148001 A148002 A148003

Adjacent sequences: A147997 A147998 A147999 * A148001 A148002 A148003

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved