A213493 Number of (w,x,y) with all terms in {0,...,n} and the numbers w,x,y,|w-x|,|x-y|,|y-w| distinct.

0, 0, 0, 0, 0, 0, 12, 48, 96, 204, 300, 480, 684, 972, 1260, 1692, 2124, 2700, 3288, 4044, 4812, 5784, 6744, 7932, 9144, 10584, 12024, 13752, 15480, 17496, 19524, 21864, 24216, 26916, 29604, 32664, 35748, 39204, 42660, 46548, 50436, 54756

Offset: 0

Author

Clark Kimberling, Jun 13 2012

Keywords

• nonn
• easy

Comments

Every term is divisible by 12; see A213494.

For a guide to related sequences, see A212959.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,-2,0,0,1,1,-1).

Crossrefs

Cf. A212959, A213494.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Length[Union[{w, x, y, Abs[w - x], Abs[x - y], Abs[y - w]}]] ==
6, s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]]   (* this sequence *)
m/12  (* A213494 *)
LinearRecurrence[{1, 1, 0, 0, -2, 0, 0, 1, 1, -1}, {0, 0, 0, 0, 0, 0, 12, 48, 96, 204}, 60]

Formula

a(n) = a(n-1) + a(n-2) - 2*a(n-5) + a(n-8) + a(n-9) - a(n-10).

G.f.: 12*(x^6 + 3*x^7 + 3*x^8 + 5*x^9)/(1 - x - x^2 + 2*x^5 - x^8 - x^9 + x^10).