A212981 - OEIS

%I #20 Jun 13 2015 00:54:15

%S 0,2,8,21,43,77,125,190,274,380,510,667,853,1071,1323,1612,1940,2310,

%T 2724,3185,3695,4257,4873,5546,6278,7072,7930,8855,9849,10915,12055,

%U 13272,14568,15946,17408,18957,20595,22325,24149,26070,28090

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

%C For a guide to related sequences, see A212959.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).

%F a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5).

%F G.f.: f(x)/g(x), where f(x)=2*x + 2*x^2 + x^3 and g(x)=(1+x)*(1-x)^4.

%F a(n) = (20*n^3+42*n^2+28*n+3*(1-(-1)^n))/48. - _Luce ETIENNE_, Feb 17 2015

%t t = Compile[{{n, _Integer}}, Module[{s = 0},

%t (Do[If[w <= x + y && x < y, s = s + 1],

%t {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];

%t m = Map[t[#] &, Range[0, 60]]   (* A212981 *)

%t LinearRecurrence[{3,-2,-2,3,-1},{0,2,8,21,43},50] (* _Harvey P. Dale_, Jul 31 2013 *)

%Y Cf. A212959.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Jun 04 2012