cp's OEIS Frontend

A213484 Number of (w,x,y) with all terms in {0,...,n} and |w-x| + |x-y| + |y-w| >= w+x+y.

%I A213484 #14 Apr 25 2024 09:28:14
%S A213484 1,4,7,10,16,25,34,43,55,70,85,100,118,139,160,181,205,232,259,286,
%T A213484 316,349,382,415,451,490,529,568,610,655,700,745,793,844,895,946,1000,
%U A213484 1057,1114,1171,1231,1294,1357,1420,1486,1555,1624,1693,1765
%N A213484 Number of (w,x,y) with all terms in {0,...,n} and |w-x| + |x-y| + |y-w| >= w+x+y.
%C A213484 a(n) + A213485(n) = (n+1)^3.
%C A213484 For a guide to related sequences, see A212959.
%H A213484 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-4,4,-3,1).
%F A213484 a(n) = 3*a(n-1) - 4*a(n-2) + 4*a(n-3) - 3*a(n-4) + a(n-5).
%F A213484 G.f.: (1 + x - x^2 + x^3 + x^4)/((1 - x)^3 (1 + x^2)).
%F A213484 From _Ayoub Saber Rguez_, Dec 31 2021: (Start)
%F A213484 a(n) + A213485(n) = (n+1)^3.
%F A213484 a(n) = 3*A054925(n+1) + 1.
%F A213484 a(n) = 3*(A192447(n+1)/2) + 1.
%F A213484 a(n) = (3*n^2 + 3*n + 4 + 3*((n+1) mod 4 - (n+1) mod 2))/4. (End)
%t A213484 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A213484 (Do[If[w + x + y == Abs[w - x] + Abs[x - y] + Abs[y - w],
%t A213484 s = s + 1],
%t A213484 {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213484 Map[t[#] &, Range[0, 60]]   (* A213484 *)
%Y A213484 Cf. A212959.
%K A213484 nonn,easy
%O A213484 0,2
%A A213484 _Clark Kimberling_, Jun 13 2012