A212966 Number of (w,x,y) with all terms in {0,...,n} and 2*w=range{w,x,y}.

1, 1, 3, 8, 10, 12, 23, 25, 29, 44, 48, 52, 73, 77, 83, 108, 114, 120, 151, 157, 165, 200, 208, 216, 257, 265, 275, 320, 330, 340, 391, 401, 413, 468, 480, 492, 553, 565, 579, 644, 658, 672, 743, 757, 773, 848, 864, 880, 961, 977, 995, 1080, 1098

Offset: 0

Author

Clark Kimberling, Jun 02 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A212959.

Links

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

Crossrefs

Cf. A212959.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[2 w == Max[w, x, y] - Min[w, x, y], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
Map[t[#] &, Range[0, 60]]   (* A212966 *)

Formula

a(n) = a(n-2)+2*a(n-3)-2*a(n-5)-a(n-6)+a(n-8).

G.f.: f(x)/g(x), where f(x)=1 + x + 2*x^2 + 5*x^3 + 5*x^4 and g(x)=(1+x)((1-x)^3)(1+x+x^2)^2.