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A211618 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and 2w+x+y>1.

%I A211618 #10 Dec 04 2017 11:53:54
%S A211618 0,3,24,89,218,439,772,1245,1878,2699,3728,4993,6514,8319,10428,12869,
%T A211618 15662,18835,22408,26409,30858,35783,41204,47149,53638,60699,68352,
%U A211618 76625,85538,95119,105388,116373,128094,140579,153848,167929,182842,198615,215268
%N A211618 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and 2w+x+y>1.
%C A211618 For a guide to related sequences, see A211422.
%H A211618 Colin Barker, <a href="/A211618/b211618.txt">Table of n, a(n) for n = 0..1000</a>
%H A211618 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F A211618 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 A211618 From _Colin Barker_, Dec 04 2017: (Start)
%F A211618 G.f.: x*(3 + 15*x + 23*x^2 + 5*x^3 + 2*x^4) / ((1 - x)^4*(1 + x)).
%F A211618 a(n) = 4*n^3 - 3*n^2 + 3*n - 2 for n>0 and even.
%F A211618 a(n) = 4*n^3 - 3*n^2 + 3*n - 1 for n odd.
%F A211618 (End)
%t A211618 t = Compile[{{u, _Integer}},
%t A211618    Module[{s = 0}, (Do[If[2 w + x + y > 1,
%t A211618          s = s + 1], {w, #}, {x, #}, {y, #}] &[
%t A211618       Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
%t A211618 Map[t[#] &, Range[0, 70]]  (* A211618 *)
%t A211618 FindLinearRecurrence[%]
%t A211618 (* _Peter J. C. Moses_, Apr 13 2012 *)
%t A211618 Join[{0},LinearRecurrence[{3, -2, -2, 3, -1},{3, 24, 89, 218, 439},35]] (* _Ray Chandler_, Aug 02 2015 *)
%o A211618 (PARI) concat(0, Vec(x*(3 + 15*x + 23*x^2 + 5*x^3 + 2*x^4) / ((1 - x)^4*(1 + x)) + O(x^40))) \\ _Colin Barker_, Dec 04 2017
%Y A211618 Cf. A211422.
%K A211618 nonn,easy
%O A211618 0,2
%A A211618 _Clark Kimberling_, Apr 16 2012