A212749 Number of (w,x,y,z) with all terms in {0,...,n} and at least one of these conditions holds: w=R, x

1, 14, 70, 222, 537, 1116, 2056, 3512, 5605, 8550, 12486, 17694, 24325, 32732, 43072, 55776, 71001, 89262, 110710, 135950, 165121, 198924, 237480, 281592, 331357, 387686, 450646, 521262, 599565, 686700, 782656, 888704, 1004785

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]] (* A212749  *)
(* 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.: ( -1-12*x-40*x^2-60*x^3-37*x^4-12*x^5 ) / ( (1+x)^3*(x-1)^5 ).