A212741 - OEIS

%I #14 Jun 13 2015 00:54:14

%S 1,15,79,239,593,1199,2239,3759,6049,9119,13391,18815,25969,34719,

%T 45823,59039,75329,94319,117199,143439,174481,209615,250559,296399,

%U 349153,407679,474319,547679,630449,720959,822271,932415,1054849

%N Number of (w,x,y,z) with all terms in {0,...,n} and max{w,x,y,z}>=2*min{w,x,y,z}.

%C Also the number of (w,x,y,z) with all terms in {0,...,n} and at least one term <= range{w,x,y,z}.

%C Every term is odd.

%C a(n)+A212740(n)=n^4.

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

%F G.f.: ( -1-13*x-47*x^2-57*x^3-47*x^4-3*x^5-x^6+x^7 ) / ( (1+x)^3*(x-1)^5 ).

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

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

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

%t Map[t[#] &, Range[0, 40]]   (* A212741 *)

%Y Cf. A211795, A212743.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, May 26 2012