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A211627 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and w+5x+5y>0.

%I A211627 #10 Dec 05 2017 08:19:13
%S A211627 0,4,32,108,256,492,854,1360,2034,2900,3965,5285,6869,8741,10925,
%T A211627 13419,16297,19559,23229,27331,31854,36890,42430,48498,55118,62270,
%U A211627 70064,78482,87548,97286,107667,118819,130715,143379,156835,171045,186155,202129,218991
%N A211627 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and w+5x+5y>0.
%C A211627 For a guide to related sequences, see A211422.
%H A211627 Colin Barker, <a href="/A211627/b211627.txt">Table of n, a(n) for n = 0..1000</a>
%H A211627 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,2,-4,2,0,0,-1,2,-1).
%F A211627 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-5) - 4*a(n-6) + 2*a(n-7) - a(n-10) + 2*a(n-11) - a(n-12) for n>11.
%F A211627 G.f.: x*(4 + 24*x + 48*x^2 + 72*x^3 + 88*x^4 + 118*x^5 + 96*x^6 + 72*x^7 + 48*x^8 + 23*x^9 + 7*x^10) / ((1 - x)^4*(1 + x + x^2 + x^3 + x^4)^2). - _Colin Barker_, Dec 05 2017
%t A211627 t = Compile[{{u, _Integer}},
%t A211627    Module[{s = 0}, (Do[If[w + 5 x + 5 y > 0,
%t A211627          s = s + 1], {w, #}, {x, #}, {y, #}] &[
%t A211627       Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
%t A211627 Map[t[#] &, Range[0, 60]]  (* A211627 *)
%t A211627 FindLinearRecurrence[%]
%t A211627 (* _Peter J. C. Moses_, Apr 13 2012 *)
%t A211627 LinearRecurrence[{2, -1, 0, 0, 2, -4, 2, 0, 0, -1, 2, -1},{0, 4, 32, 108, 256, 492, 854, 1360, 2034, 2900, 3965, 5285},36] (* _Ray Chandler_, Aug 02 2015 *)
%o A211627 (PARI) concat(0, Vec(x*(4 + 24*x + 48*x^2 + 72*x^3 + 88*x^4 + 118*x^5 + 96*x^6 + 72*x^7 + 48*x^8 + 23*x^9 + 7*x^10) / ((1 - x)^4*(1 + x + x^2 + x^3 + x^4)^2) + O(x^40))) \\ _Colin Barker_, Dec 05 2017
%Y A211627 Cf. A211422.
%K A211627 nonn,easy
%O A211627 0,2
%A A211627 _Clark Kimberling_, Apr 17 2012