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A212743 Number of (w,x,y,z) with all terms in {0,...,n} and max{w,x,y,z}>2*min{w,x,y,z}. 4

%I

%S 0,14,64,224,528,1134,2064,3584,5680,8750,12720,18144,24864,33614,

%T 44128,57344,72864,91854,113760,140000,169840,204974,244464,290304,

%U 341328,399854,464464,537824,618240,708750,807360,917504,1036864

%N Number of (w,x,y,z) with all terms in {0,...,n} and max{w,x,y,z}>2*min{w,x,y,z}.

%C Also the number of (w,x,y,z) with all terms in {0,...,n} and at least one term < range{w,x,y,z}.

%C Every term is even.

%C a(n)+A212742(n)=n^4.

%C For a guide to related sequences, see A211795.

%F a(n)=2*a(n-1)+2*a(n-2)-6*a(n-3)+6*a(n-5)-2*a(n-6)-2*a(n-7)+a(n-8).

%F G.f.: f(x)/g(x), where f(x)=-7*x-18*x^2-34*x^3-18*x^4-7*x^5 and g(x)=((1-x)^5)*(1+x)^3.

%t t = Compile[{{n, _Integer}}, Module[{s = 0},

%t (Do[If[Max[w, x, y, z] > 2 Min[w, x, y, z], s = s + 1],

%t {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];

%t Map[t[#] &, Range[0, 40]] (* A212743 *)

%t %/2 (* integers *)

%Y Cf. A211795.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, May 26 2012

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Last modified April 15 01:24 EDT 2021. Contains 342974 sequences. (Running on oeis4.)