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A211629 Number of ordered triples (w,x,y) with all terms in {-n, ..., -1, 1, ..., n} and 4w + x + y > 0.

%I A211629 #13 Dec 06 2017 04:54:32
%S A211629 0,4,31,105,252,492,851,1353,2024,2884,3959,5273,6852,8716,10891,
%T A211629 13401,16272,19524,23183,27273,31820,36844,42371,48425,55032,62212,
%U A211629 69991,78393,87444,97164,107579,118713,130592,143236,156671,170921,186012,201964,218803
%N A211629 Number of ordered triples (w,x,y) with all terms in {-n, ..., -1, 1, ..., n} and 4w + x + y > 0.
%C A211629 For a guide to related sequences, see A211422.
%H A211629 Colin Barker, <a href="/A211629/b211629.txt">Table of n, a(n) for n = 0..1000</a>
%H A211629 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,1,-3,3,-1).
%F A211629 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-4) - 3*a(n-5) + 3*a(n-6) - a(n-7) for n > 6.
%F A211629 G.f.: x*(4 + 19*x + 24*x^2 + 26*x^3 + 16*x^4 + 7*x^5) / ((1 - x)^4*(1 + x)*(1 + x^2)). - _Colin Barker_, Dec 05 2017
%t A211629 t = Compile[{{u, _Integer}},
%t A211629    Module[{s = 0}, (Do[If[4 w + x + y > 0,
%t A211629          s = s + 1], {w, #}, {x, #}, {y, #}] &[
%t A211629       Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
%t A211629 Map[t[#] &, Range[0, 60]]  (* A211629 *)
%t A211629 FindLinearRecurrence[%]
%t A211629 (* _Peter J. C. Moses_, Apr 13 2012 *)
%t A211629 LinearRecurrence[{3, -3, 1, 1, -3, 3, -1},{0, 4, 31, 105, 252, 492, 851},36] (* _Ray Chandler_, Aug 02 2015 *)
%o A211629 (PARI) concat(0, Vec(x*(4 + 19*x + 24*x^2 + 26*x^3 + 16*x^4 + 7*x^5) / ((1 - x)^4*(1 + x)*(1 + x^2)) + O(x^40))) \\ _Colin Barker_, Dec 05 2017
%Y A211629 Cf. A211422.
%K A211629 nonn,easy
%O A211629 0,2
%A A211629 _Clark Kimberling_, Apr 17 2012