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A211619 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and 2w+x+y>2.

%I A211619 #10 Dec 04 2017 16:12:55
%S A211619 0,1,18,73,192,395,710,1157,1764,2551,3546,4769,6248,8003,10062,12445,
%T A211619 15180,18287,21794,25721,30096,34939,40278,46133,52532,59495,67050,
%U A211619 75217,84024,93491,103646,114509,126108,138463,151602,165545,180320,195947,212454
%N A211619 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and 2w+x+y>2.
%C A211619 For a guide to related sequences, see A211422.
%H A211619 Colin Barker, <a href="/A211619/b211619.txt">Table of n, a(n) for n = 0..1000</a>
%H A211619 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F A211619 a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5) for n>6.
%F A211619 From _Colin Barker_, Dec 04 2017: (Start)
%F A211619 G.f.: x*(1 + 15*x + 21*x^2 + 11*x^3 - 2*x^4 + 2*x^5) / ((1 - x)^4*(1 + x)).
%F A211619 a(n) = 4*n^3 - 5*n^2 + 5*n - 4 for n>1 and even.
%F A211619 a(n) = 4*n^3 - 5*n^2 + 5*n - 5 for n>1 and odd.
%F A211619 (End)
%t A211619 t = Compile[{{u, _Integer}},
%t A211619    Module[{s = 0}, (Do[If[2 w + x + y > 2,
%t A211619          s = s + 1], {w, #}, {x, #}, {y, #}] &[
%t A211619       Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
%t A211619 Map[t[#] &, Range[0, 70]]  (* A211619 *)
%t A211619 FindLinearRecurrence[%]
%t A211619 (* _Peter J. C. Moses_, Apr 13 2012 *)
%t A211619 Join[{0, 1},LinearRecurrence[{3, -2, -2, 3, -1},{18, 73, 192, 395, 710},34]] (* _Ray Chandler_, Aug 02 2015 *)
%o A211619 (PARI) concat(0, Vec(x*(1 + 15*x + 21*x^2 + 11*x^3 - 2*x^4 + 2*x^5) / ((1 - x)^4*(1 + x)) + O(x^40))) \\ _Colin Barker_, Dec 04 2017
%Y A211619 Cf. A211422.
%K A211619 nonn,easy
%O A211619 0,3
%A A211619 _Clark Kimberling_, Apr 16 2012