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%I #13 Jun 13 2015 00:54:14
%S 1,2,17,32,97,162,337,512,881,1250,1921,2592,3697,4802,6497,8192,
%T 10657,13122,16561,20000,24641,29282,35377,41472,49297,57122,66977,
%U 76832,89041,101250,116161,131072,149057,167042,188497,209952,235297
%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 the differences w-x, x-y, y-z all even.
%C a(n)+A212743(n) = n^4.
%C For a guide to related sequences, see A211795.
%H <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 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.: -(1+x^2)*(x^4+10*x^2+1) / ( (1+x)^3*(x-1)^5 ).
%F a(n) = A212740(n+1) for n>=0.
%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]] (* A212742 *)
%t LinearRecurrence[{2,2,-6,0,6,-2,-2,1},{1,2,17,32,97,162,337,512},40] (* _Harvey P. Dale_, May 14 2013 *)
%Y Cf. A211795.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, May 26 2012
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