A148161 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, 1, -1), (1, 0, 0)}.

1, 1, 2, 4, 11, 31, 86, 262, 787, 2442, 7677, 24581, 80379, 261809, 867313, 2890472, 9684442, 32683354, 110898717, 379064856, 1297810439, 4466393711, 15433476163, 53483388756, 185962286216, 648576840593, 2269821822857, 7957275602226, 27969780462858, 98546712605786, 347890004162970, 1230552458589243

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..220

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

Maple

Steps:= [[-1, -1, 0], [-1, 1, 1], [0, 1, -1], [1, 0, 0] ]:
f:= proc(n, p) option remember;
  if n <= min(p) then return 4^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, Aug 22 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, j, k, -1 + n] + aux[i, -1 + 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: A002387 A325922 A148160 * A263375 A148162 A148163

Adjacent sequences: A148158 A148159 A148160 * A148162 A148163 A148164

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved