A212751 Number of (w,x,y,z) with all terms in {0,...,n} and at least one of these conditions holds: w=R, x=R, y=R, z

1, 14, 70, 198, 477, 924, 1696, 2768, 4405, 6510, 9486, 13134, 18025, 23828, 31312, 39984, 50841, 63198, 78310, 95270, 115621, 138204, 164880, 194208, 228397, 265694, 308686, 355278, 408465, 465780, 530656, 600224, 678385, 761838

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]] (* A212751 *)
(* 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^2-36*x^3-25*x^4+12*x^5 ) / ( (1+x)^3*(x-1)^5 ).