A149663 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), (0, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 61, 241, 1013, 4073, 17069, 73505, 316133, 1361337, 5980189, 26406801, 116548949, 518274729, 2322720077, 10418420609, 46852187525, 211863806873, 960661273085, 4360754376177, 19857020638645, 90694294866057, 414765463767725, 1899929428731233, 8724174474617573, 40124073832013433

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..200

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], [0, 0, -1], [0, 1, -1], [1, 1, 1]]:
f:= proc(n, p) option remember; local t;
  if n <= min(p) then return 5^n fi;
  add(procname(n-1, t), t=remove(has, map(`+`, Steps, p), -1));
end proc: A:= map(f, [$0..100], [0, 0, 0]); # Robert Israel, Aug 11 2019

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, -1 + 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: A273680 A273759 A149662 * A149664 A149665 A149666

Adjacent sequences: A149660 A149661 A149662 * A149664 A149665 A149666

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved