A212741 Number of (w,x,y,z) with all terms in {0,...,n} and max{w,x,y,z}>=2*min{w,x,y,z}.

1, 15, 79, 239, 593, 1199, 2239, 3759, 6049, 9119, 13391, 18815, 25969, 34719, 45823, 59039, 75329, 94319, 117199, 143439, 174481, 209615, 250559, 296399, 349153, 407679, 474319, 547679, 630449, 720959, 822271, 932415, 1054849

Offset: 0

Author

Clark Kimberling, May 26 2012

Keywords

• nonn
• easy

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 odd.

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

For a guide to related sequences, see A211795.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1)

Crossrefs

Cf. A211795, A212743.

Programs

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]]   (* A212741 *)

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.: ( -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 ).