A211625 Number of ordered triples (w,x,y) with all terms in {-n,...,-1,1,...,n} and w+3x+3y>0.

0, 4, 32, 104, 250, 492, 845, 1349, 2021, 2871, 3949, 5267, 6830, 8698, 10878, 13370, 16244, 19502, 23139, 27235, 31787, 36785, 42319, 48381, 54956, 62144, 69932, 78300, 87358, 97088, 107465, 118609, 130497, 143099, 156545, 170807, 185850, 201814, 218666

Offset: 0

Author

Clark Kimberling, Apr 17 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A211422.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-4,2,-1,2,-1).

Crossrefs

Cf. A211422.

Programs

Mathematica

Remove["Global`*"];
t = Compile[{{u, _Integer}},
   Module[{s = 0}, (Do[If[w + 3 x + 3 y > 0,
         s = s + 1], {w, #}, {x, #}, {y, #}] &[
      Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &, Range[0, 60]]  (* A211625 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
LinearRecurrence[{2, -1, 2, -4, 2, -1, 2, -1},{0, 4, 32, 104, 250, 492, 845, 1349},36] (* Ray Chandler, Aug 02 2015 *)

PARI

concat(0, Vec(x*(7*x^6+23*x^5+48*x^4+66*x^3+44*x^2+24*x+4)/((x-1)^4*(x^2+x+1)^2) + O(x^100))) \\ Colin Barker, Nov 17 2015

Formula

a(n) = 2*a(n-1)-a(n-2)+2*a(n-3)-4*a(n-4)+2*a(n-5)-a(n-6)+2*a(n-7)-a(n-8).

G.f.: x*(7*x^6+23*x^5+48*x^4+66*x^3+44*x^2+24*x+4) / ((x-1)^4*(x^2+x+1)^2). - Colin Barker, Nov 17 2015