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A212974 Number of (w,x,y) with all terms in {0,...,n} and w>floor((x+y)/3).

%I A212974 #19 Jan 05 2025 12:31:13
%S A212974 0,4,15,37,75,132,212,320,459,633,847,1104,1408,1764,2175,2645,3179,
%T A212974 3780,4452,5200,6027,6937,7935,9024,10208,11492,12879,14373,15979,
%U A212974 17700,19540,21504,23595,25817,28175,30672,33312,36100,39039,42133
%N A212974 Number of (w,x,y) with all terms in {0,...,n} and w>floor((x+y)/3).
%C A212974 a(n)+A212973(n) = (n+1)^3.
%C A212974 For a guide to related sequences, see A212959.
%H A212974 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,2,-3,3,-1).
%F A212974 a(n) = 3*a(n-1)-3*a(n-2)+2*a(n-3)-3*a(n-4)+3*a(n-5)-a(n-6).
%F A212974 G.f.: x*(4 + 3*x + 4*x^2 + x^3)/((1 + x + x^2)*(1 - x)^4).
%t A212974 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212974 (Do[If[w > Floor[(x + y)/3], s = s + 1],
%t A212974 {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A212974 m = Map[t[#] &, Range[0, 60]]   (* A212974 *)
%Y A212974 Cf. A212959, A212973.
%K A212974 nonn,easy
%O A212974 0,2
%A A212974 _Clark Kimberling_, Jun 03 2012