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A212503 Number of (w,x,y,z) with all terms in {1,...,n} and w<2x and y<2z.

%I A212503 #15 Jan 05 2025 05:53:48
%S A212503 0,1,9,49,144,361,729,1369,2304,3721,5625,8281,11664,16129,21609,
%T A212503 28561,36864,47089,59049,73441,90000,109561,131769,157609,186624,
%U A212503 219961,257049,299209,345744,398161,455625,519841,589824,667489,751689
%N A212503 Number of (w,x,y,z) with all terms in {1,...,n} and w<2x and y<2z.
%C A212503 For a guide to related sequences, see A211795.
%H A212503 <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 A212503 a(n) = (A077043(n))^2.
%F A212503 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 A212503 G.f.: x*(1+x+x^2)*(1+6*x+22*x^2+6*x^3+x^4)/((1+x)^3*(1-x)^5). [_Bruno Berselli_, May 31 2012]
%t A212503 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212503 (Do[If[w < 2 x && y < 2 z, s = s + 1],
%t A212503 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212503 Map[t[#] &, Range[0, 40]]   (* A212503 *)
%t A212503 LinearRecurrence[{2,2,-6,0,6,-2,-2,1},{0,1,9,49,144,361,729,1369},40] (* _Harvey P. Dale_, Jun 14 2017 *)
%Y A212503 Cf. A211795.
%K A212503 nonn,easy
%O A212503 0,3
%A A212503 _Clark Kimberling_, May 19 2012