A148382 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, 0, 1), (0, 1, 0), (1, -1, 1), (1, 0, -1)}.

1, 1, 2, 5, 16, 49, 171, 609, 2256, 8551, 33397, 131427, 529260, 2149049, 8851768, 36730319, 154130790, 650143287, 2767497613, 11832774631, 50953284486, 220254234487, 957671050740, 4177306152161, 18311313390468, 80489613677085, 355279416601419, 1571992334010585, 6980467436390932

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..100

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

Maple

b:= proc(n, l) option remember;
      `if`(min(l[])<0, 0, `if`(n=0, 1, add (b(n-1, l+s),
       s=[[-1, -1, -1], [-1, 0, 1], [0, 1, 0], [1, -1, 1], [1, 0, -1]])))
    end:
a:= n-> b(n, [0$3]):
seq (a(n), n=0..30);  # Alois P. Heinz, Jun 01 2012

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A148381 A334293 A278274 * A148383 A148384 A148385

Adjacent sequences: A148379 A148380 A148381 * A148383 A148384 A148385

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved