A212504 - OEIS

%I #16 Mar 09 2016 05:26:57

%S 0,0,0,7,24,76,162,333,576,976,1500,2275,3240,4572,6174,8281,10752,

%T 13888,17496,21951,27000,33100,39930,48037,57024,67536,79092,92443,

%U 107016,123676,141750,162225,184320,209152,235824,265591,297432

%N Number of (w,x,y,z) with all terms in {1,...,n} and w<2x and y>2z.

%C For a guide to related sequences, see A211795.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).

%F a(n) = 2a(n-1)+2a(n-2)-6a(n-3)+6a(n-5)-2a(n-6)-2a(n-7)+a(n-8).

%F From _Alois P. Heinz_, May 31 2012: (Start)

%F a(n) = A077043(n) * A002620(n-1) = ceiling(n^2*3/4) * floor((n-1)^2/4).

%F G.f.: x^3*(7+10*x+14*x^2+4*x^3+x^4) / ((x+1)^3*(1-x)^5). (End)

%p A212504:=n->ceil(3*n^2/4)*floor((n-1)^2/4); seq(A212504(n), n=0..40); # _Wesley Ivan Hurt_, Jan 24 2014

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

%t (Do[If[w < 2 x && y > 2 z, s = s + 1],

%t {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];

%t Map[t[#] &, Range[0, 40]]   (* A212504 *)

%Y Cf. A211795.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, May 19 2012