A149585 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), (-1, 0, 1), (0, 0, -1), (1, 1, 1)}

1, 1, 5, 15, 55, 203, 791, 3041, 12057, 48249, 194705, 790373, 3237213, 13323957, 55078721, 228709819, 953594747, 3988265595, 16730145283, 70382381531, 296830291631, 1254604475451, 5314036803363, 22552374316543, 95878895567139, 408287637231539, 1741343710323743, 7437497858831271

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..225

Alin Bostan and Manuel Kauers, Automatic Classification of Restricted Lattice Walks, arXiv:0811.2899 [math.CO], 2009.

Maple

Steps:= [[-1, -1, 0], [-1, -1, 1], [-1, 0, 1], [0, 0, -1], [1, 1, 1] ]:
f:= proc(n, p) option remember;
  if n <= min(p) then return 5^n fi;
  add(procname(n-1, t), t=remove(has, map(`+`, Steps, p), -1));
end proc:
map(f, [$0..30], [0, 0, 0]); # Robert Israel, Feb 27 2022

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[i, j, 1 + k, -1 + n] + aux[1 + 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: A123011 A006358 A054108 * A114947 A316104 A149586

Adjacent sequences: A149582 A149583 A149584 * A149586 A149587 A149588

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved