A148410 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, 1, -1)}.

1, 1, 2, 5, 17, 56, 204, 779, 3083, 12542, 51867, 218851, 937428, 4066279, 17819039, 78771159, 351148071, 1576762625, 7124754861, 32369976554, 147797541104, 677966771333, 3123008282073, 14439960175164, 66992611362021, 311781381899059, 1455300136591569, 6811383379597123, 31959257776835476

Offset

0,3

Links

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

A. Bostan and M. Kauers, Automatic Classification of Restricted Lattice Walks, arXiv:0811.2899 [math.CO], 2008-2009.

Maple

Steps:= [[-1, -1, -1], [-1, 0, 1], [0, 1, 0], [1, -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: map(f, [$0..40], [0, 0, 0]); # Robert Israel, Dec 26 2018

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[-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: A042671 A180148 A241133 * A190531 A148411 A149987

Adjacent sequences: A148407 A148408 A148409 * A148411 A148412 A148413

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved