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A211622 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and w+2x+3y>1.

%I A211622 #12 Dec 05 2017 06:29:56
%S A211622 0,3,26,94,229,457,800,1284,1931,2767,3814,5098,6641,8469,10604,13072,
%T A211622 15895,19099,22706,26742,31229,36193,41656,47644,54179,61287,68990,
%U A211622 77314,86281,95917,106244,117288,129071,141619,154954,169102,184085,199929,216656
%N A211622 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and w+2x+3y>1.
%C A211622 For a guide to related sequences, see A211422.
%H A211622 Colin Barker, <a href="/A211622/b211622.txt">Table of n, a(n) for n = 0..1000</a>
%H A211622 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F A211622 a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5) for n>5.
%F A211622 From _Colin Barker_, Dec 05 2017: (Start)
%F A211622 G.f.: x*(3 + 17*x + 22*x^2 + 5*x^3 + x^4) / ((1 - x)^4*(1 + x)).
%F A211622 a(n) = (8*n^3 - 4*n^2 + 3*n - 2) / 2 for n>0 and even.
%F A211622 a(n) = (16*n^3 - 8*n^2 + 6*n - 2) / 4 for n odd.
%F A211622 (End)
%t A211622 t = Compile[{{u, _Integer}},
%t A211622    Module[{s = 0}, (Do[If[w + 2 x + 3 y > 1,
%t A211622          s = s + 1], {w, #}, {x, #}, {y, #}] &[
%t A211622       Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
%t A211622 Map[t[#] &, Range[0, 70]]  (* A211622 *)
%t A211622 FindLinearRecurrence[%]
%t A211622 (* _Peter J. C. Moses_, Apr 13 2012 *)
%t A211622 Join[{0},LinearRecurrence[{3, -2, -2, 3, -1},{3, 26, 94, 229, 457},35]] (* _Ray Chandler_, Aug 02 2015 *)
%o A211622 (PARI) concat(0, Vec(x*(3 + 17*x + 22*x^2 + 5*x^3 + x^4) / ((1 - x)^4*(1 + x)) + O(x^40))) \\ _Colin Barker_, Dec 05 2017
%Y A211622 Cf. A211422.
%K A211622 nonn,easy
%O A211622 0,2
%A A211622 _Clark Kimberling_, Apr 16 2012