A212754 Number of (w,x,y,z) with all terms in {0,...,n} and at least one of these conditions holds: wR, y>R, z>R, where R = max{w,x,y,z} - min{w,x,y,z}.

0, 8, 53, 184, 472, 1008, 1905, 3296, 5336, 8200, 12085, 17208, 23808, 32144, 42497, 55168, 70480, 88776, 110421, 135800, 165320, 199408, 238513, 283104, 333672, 390728, 454805, 526456, 606256, 694800, 792705, 900608, 1019168

Offset: 0

Author

Clark Kimberling, May 28 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A211795.

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-5,0,5,-4,1).

Crossrefs

Cf. A211795.

Programs

Mathematica

t = Compile[{{n, _Integer}},
Module[{s = 0}, (Do[
If[(w < # || x > # || y > # || z > #) &[
Max[w, x, y, z] - Min[w, x, y, z]], s++], {w, 0, n},
{x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 40]] (* A212754 *)
(* Peter J. C. Moses, May 24 2012 *)

Formula

a(n)=4*a(n-1)-5*a(n-2)+5*a(n-4)-4*a(n-5)+a(n-6).

G.f.: -x*(8+21*x+12*x^2+x^3) / ( (1+x)*(x-1)^5 ).