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A212982 Number of (w,x,y) with all terms in {0,...,n} and w and x<=y.

%I A212982 #12 Jan 28 2016 06:02:19
%S A212982 0,3,11,27,53,92,146,218,310,425,565,733,931,1162,1428,1732,2076,2463,
%T A212982 2895,3375,3905,4488,5126,5822,6578,7397,8281,9233,10255,11350,12520,
%U A212982 13768,15096,16507,18003,19587,21261,23028,24890,26850,28910,31073,33341,35717
%N A212982 Number of (w,x,y) with all terms in {0,...,n} and w<x+y and x<=y.
%C A212982 For a guide to related sequences, see A212959.
%H A212982 Colin Barker, <a href="/A212982/b212982.txt">Table of n, a(n) for n = 0..1000</a>
%H A212982 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F A212982 a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5).
%F A212982 G.f.: f(x)/g(x), where f(x)=3*x + 2*x^2 and g(x)=(1+x)*(1-x)^4.
%F A212982 From _Colin Barker_, Jan 28 2016: (Start)
%F A212982 a(n) = (20*n^3+66*n^2+52*n-3*(-1)^n+3)/48.
%F A212982 a(n) = (10*n^3+33*n^2+26*n)/24 for n even.
%F A212982 a(n) = (10*n^3+33*n^2+26*n+3)/24 for n odd.
%F A212982 (End)
%t A212982 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212982 (Do[If[w < x + y && x <= y, s = s + 1],
%t A212982 {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A212982 m = Map[t[#] &, Range[0, 60]]   (* A212982 *)
%o A212982 (PARI) concat(0, Vec(x*(3+2*x)/((1-x)^4*(1+x)) + O(x^100))) \\ _Colin Barker_, Jan 28 2016
%Y A212982 Cf. A212959.
%K A212982 nonn,easy
%O A212982 0,2
%A A212982 _Clark Kimberling_, Jun 04 2012