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A211625 Number of ordered triples (w,x,y) with all terms in {-n,...,-1,1,...,n} and w+3x+3y>0.

%I A211625 #13 Nov 17 2015 14:29:43
%S A211625 0,4,32,104,250,492,845,1349,2021,2871,3949,5267,6830,8698,10878,
%T A211625 13370,16244,19502,23139,27235,31787,36785,42319,48381,54956,62144,
%U A211625 69932,78300,87358,97088,107465,118609,130497,143099,156545,170807,185850,201814,218666
%N A211625 Number of ordered triples (w,x,y) with all terms in {-n,...,-1,1,...,n} and w+3x+3y>0.
%C A211625 For a guide to related sequences, see A211422.
%H A211625 Colin Barker, <a href="/A211625/b211625.txt">Table of n, a(n) for n = 0..1000</a>
%H A211625 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,2,-4,2,-1,2,-1).
%F A211625 a(n) = 2*a(n-1)-a(n-2)+2*a(n-3)-4*a(n-4)+2*a(n-5)-a(n-6)+2*a(n-7)-a(n-8).
%F A211625 G.f.: x*(7*x^6+23*x^5+48*x^4+66*x^3+44*x^2+24*x+4) / ((x-1)^4*(x^2+x+1)^2). - _Colin Barker_, Nov 17 2015
%t A211625 Remove["Global`*"];
%t A211625 t = Compile[{{u, _Integer}},
%t A211625    Module[{s = 0}, (Do[If[w + 3 x + 3 y > 0,
%t A211625          s = s + 1], {w, #}, {x, #}, {y, #}] &[
%t A211625       Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
%t A211625 Map[t[#] &, Range[0, 60]]  (* A211625 *)
%t A211625 FindLinearRecurrence[%]
%t A211625 (* _Peter J. C. Moses_, Apr 13 2012 *)
%t A211625 LinearRecurrence[{2, -1, 2, -4, 2, -1, 2, -1},{0, 4, 32, 104, 250, 492, 845, 1349},36] (* _Ray Chandler_, Aug 02 2015 *)
%o A211625 (PARI) concat(0, Vec(x*(7*x^6+23*x^5+48*x^4+66*x^3+44*x^2+24*x+4)/((x-1)^4*(x^2+x+1)^2) + O(x^100))) \\ _Colin Barker_, Nov 17 2015
%Y A211625 Cf. A211422.
%K A211625 nonn,easy
%O A211625 0,2
%A A211625 _Clark Kimberling_, Apr 17 2012