A212752 Number of (w,x,y,z) with all terms in {0,...,n} and at least one of these conditions holds: wR, where R=max{w,x,y,z}-min{w,x,y,z}.

0, 14, 71, 238, 580, 1224, 2265, 3896, 6236, 9550, 13975, 19854, 27336, 36848, 48545, 62944, 80200, 100926, 125271, 153950, 187100, 225544, 269401, 319608, 376260, 440414, 512135, 592606, 681856, 781200, 890625, 1011584, 1144016

Offset: 0

Author

Clark Kimberling, May 27 2012

Keywords

• nonn
• easy

Comments

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.

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]] (* A212752 *)
(* Peter J. C. Moses, May 24 2012 *)

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.: -x*(14+43*x+68*x^2+46*x^3+14*x^4+x^5) / ( (1+x)^3*(x-1)^5 )