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A211626 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and w+4x+4y>0.

%I A211626 #14 Dec 05 2017 08:19:23
%S A211626 0,4,32,108,250,492,854,1360,2021,2885,3965,5285,6849,8719,10901,
%T A211626 13419,16270,19530,23198,27298,31820,36854,42392,48458,55035,62227,
%U A211626 70019,78435,87451,97185,107615,118765,130604,143264,156716,170984,186030,202000,218858
%N A211626 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and w+4x+4y>0.
%C A211626 For a guide to related sequences, see A211422.
%H A211626 Colin Barker, <a href="/A211626/b211626.txt">Table of n, a(n) for n = 0..1000</a>
%H A211626 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,2,-4,2,0,-1,2,-1).
%F A211626 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-4) - 4*a(n-5) + 2*a(n-6) - a(n-8) + 2*a(n-9) - a(n-10) for n>9.
%F A211626 G.f.: x*(4 + 24*x + 48*x^2 + 66*x^3 + 92*x^4 + 72*x^5 + 48*x^6 + 23*x^7 + 7*x^8) / ((1 - x)^4*(1 + x)^2*(1 + x^2)^2). - _Colin Barker_, Dec 05 2017
%t A211626 t = Compile[{{u, _Integer}},
%t A211626    Module[{s = 0}, (Do[If[w + 4 x + 4 y > 0,
%t A211626          s = s + 1], {w, #}, {x, #}, {y, #}] &[
%t A211626       Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
%t A211626 Map[t[#] &, Range[0, 60]]  (* A211626 *)
%t A211626 FindLinearRecurrence[%]
%t A211626 (* _Peter J. C. Moses_, Apr 13 2012 *)
%t A211626 LinearRecurrence[{2,-1,0,2,-4,2,0,-1,2,-1},{0,4,32,108,250,492,854,1360,2021,2885},40] (* _Harvey P. Dale_, Nov 29 2013 *)
%o A211626 (PARI) concat(0, Vec(x*(4 + 24*x + 48*x^2 + 66*x^3 + 92*x^4 + 72*x^5 + 48*x^6 + 23*x^7 + 7*x^8) / ((1 - x)^4*(1 + x)^2*(1 + x^2)^2) + O(x^40))) \\ _Colin Barker_, Dec 05 2017
%Y A211626 Cf. A211422.
%K A211626 nonn,easy
%O A211626 0,2
%A A211626 _Clark Kimberling_, Apr 17 2012