A149583 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, 0), (0, 0, -1), (1, -1, -1), (1, 1, 1)}

1, 1, 5, 15, 53, 213, 835, 3295, 13767, 57685, 241077, 1029629, 4454725, 19208365, 83540529, 367533441, 1617265003, 7134065021, 31725845327, 141483149299, 631238921461, 2829861186507, 12734724782627, 57333350858939, 258747925751701, 1171914417315889, 5313618366103365, 24119543507783239

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

F:= proc(x, y, z, n) option remember; local t, s, u;
     t:= 0:
     if n <= min(x, y, z) then return 5^n fi;
     for s in [[-1, -1, 0], [-1, 0, 0], [0, 0, -1], [1, -1, -1], [1, 1, 1]] do
       u:= [x, y, z]+s;
       if min(u) >= 0 then t:= t + procname(op(u), n-1) fi
     od;
     t
end proc:
seq(F(0, 0, 0, n), n=0..40); # Robert Israel, May 14 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, j, 1 + k, -1 + n] + aux[1 + i, j, 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: A335025 A149581 A149582 * A149584 A147324 A109245

Adjacent sequences: A149580 A149581 A149582 * A149584 A149585 A149586

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved