A149895 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), (0, 0, 1), (0, 1, 0), (1, 0, -1)}.

1, 2, 5, 14, 46, 159, 577, 2147, 8290, 32569, 130736, 531085, 2192274, 9130703, 38470771, 163216207, 698704886, 3007633571, 13038423868, 56779502954, 248683781581, 1093309818901, 4829390034282, 21400874540542, 95212283347723, 424764491338480, 1901372644973656, 8531453059744208

Offset

0,2

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`(n=0, 1, add((p->
      `if`(min(p[])<0, 0, b(n-1, p)))(l+s), s=[[-1, -1, 0],
      [-1, 0, 1], [0, 0, 1], [0, 1, 0], [1, 0, -1]]))
    end:
a:= n-> b(n, [0$3]):
seq(a(n), n=0..30);  # Alois P. Heinz, Apr 13 2014

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, -1 + j, k, -1 + n] + aux[i, j, -1 + 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: A006391 A240720 A232622 * A149896 A149897 A124527

Adjacent sequences: A149892 A149893 A149894 * A149896 A149897 A149898

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved