A213490 Number of (w,x,y) with all terms in {0,...,n} and the numbers w,x,y,|w-x|,|x-y| distinct.

0, 0, 0, 0, 0, 12, 38, 92, 160, 286, 422, 632, 870, 1194, 1542, 2010, 2502, 3126, 3788, 4598, 5446, 6472, 7532, 8786, 10092, 11604, 13164, 14964, 16812, 18912, 21074, 23504, 25996, 28786, 31634, 34796, 38034, 41598, 45234, 49230, 53298

Offset: 0

Author

Clark Kimberling, Jun 13 2012

Keywords

• nonn
• easy

Comments

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, A213491.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
 (Do[If[Length[Union[{w, x, y, Abs[w - x],
  Abs[x - y]}]] == 5,
s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]]   (* this sequence *)
LinearRecurrence[{1, 1, 0, 0, -2, 0, 0, 1, 1, -1}, {0, 0, 0, 0, 0, 12, 38, 92, 160, 286}, 60]
m/2 (* integers *)

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^5 + 26*x^6 + 42*x^7 + 30*x^8 + 34*x^9)/(1 - x - x^2 + 2*x^5 - x^8 - x^9 + x^10).

a(n) = (n+1)^3 - A213491(n).