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A212741 Number of (w,x,y,z) with all terms in {0,...,n} and max{w,x,y,z}>=2*min{w,x,y,z}.

%I A212741 #23 Sep 04 2025 09:20:14
%S A212741 1,15,79,239,593,1199,2239,3759,6049,9119,13391,18815,25969,34719,
%T A212741 45823,59039,75329,94319,117199,143439,174481,209615,250559,296399,
%U A212741 349153,407679,474319,547679,630449,720959,822271,932415,1054849,1187279,1333583,1491119,1664209,1849839
%N A212741 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 A212741 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 A212741 Every term is odd.
%C A212741 For a guide to related sequences, see A211795.
%H A212741 Stefano Spezia, <a href="/A212741/b212741.txt">Table of n, a(n) for n = 0..10000</a>
%H A212741 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).
%F A212741 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 A212741 G.f.: (-1-13*x-47*x^2-57*x^3-47*x^4-3*x^5-x^6+x^7 )/((1+x)^3*(x-1)^5).
%F A212741 a(n) + A212740(n) = n^4.
%F A212741 From _Stefano Spezia_, Sep 04 2025: (Start)
%F A212741 a(n) = (15 + (-1)^n + 64*n + 6*(15 + (-1)^n)*n^2 + 64*n^3 + 14*n^4)/16.
%F A212741 E.g.f.: ((8+113 x+193 x^2+74 x^3+7 x^4) Cosh[x]+(7+119 x+187 x^2+74 x^3+7 x^4) Sinh[x])/8. (End)
%t A212741 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212741 (Do[If[Max[w, x, y, z] >= 2 Min[w, x, y, z], s = s + 1],
%t A212741 {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t A212741 Map[t[#] &, Range[0, 40]]
%Y A212741 Cf. A211795, A212740, A212743.
%K A212741 nonn,easy,changed
%O A212741 0,2
%A A212741 _Clark Kimberling_, May 26 2012