A212743 Number of (w,x,y,z) with all terms in {0,...,n} and max{w,x,y,z}>2*min{w,x,y,z}.

0, 14, 64, 224, 528, 1134, 2064, 3584, 5680, 8750, 12720, 18144, 24864, 33614, 44128, 57344, 72864, 91854, 113760, 140000, 169840, 204974, 244464, 290304, 341328, 399854, 464464, 537824, 618240, 708750, 807360, 917504, 1036864

Offset

0,2

Comments

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

Every term is even.

a(n)+A212742(n)=n^4.

For a guide to related sequences, see A211795.

Links

Table of n, a(n) for n=0..32.

Formula

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).

G.f.: f(x)/g(x), where f(x)=-7*x-18*x^2-34*x^3-18*x^4-7*x^5 and g(x)=((1-x)^5)*(1+x)^3.

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Max[w, x, y, z] > 2 Min[w, x, y, z], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 40]]   (* A212743 *)
%/2 (* integers *)

Crossrefs

Cf. A211795.

Sequence in context: A069964 A275127 A074354 * A124892 A126401 A275268

Adjacent sequences: A212740 A212741 A212742 * A212744 A212745 A212746

Keyword

nonn,easy

Author

Clark Kimberling, May 26 2012

Status

approved