A211628 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and 3w+x+y>0.

0, 4, 30, 105, 249, 487, 846, 1346, 2012, 2871, 3943, 5253, 6828, 8688, 10858, 13365, 16229, 19475, 23130, 27214, 31752, 36771, 42291, 48337, 54936, 62108, 69878, 78273, 87313, 97023, 107430, 118554, 130420, 143055, 156479, 170717, 185796, 201736, 218562

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 (3,-3,2,-3,3,-1).

Crossrefs

Cf. A211422.

Programs

Mathematica

t = Compile[{{u, _Integer}},
   Module[{s = 0}, (Do[If[3 w + x + y > 0,
         s = s + 1], {w, #}, {x, #}, {y, #}] &[
      Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &, Range[0, 60]]   (* A211628 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
LinearRecurrence[{3, -3, 2, -3, 3, -1},{0, 4, 30, 105, 249, 487},36] (* Ray Chandler, Aug 02 2015 *)

PARI

concat(0, Vec(x*(4 + 18*x + 27*x^2 + 16*x^3 + 7*x^4) / ((1 - x)^4*(1 + x + x^2)) + O(x^40))) \\ Colin Barker, Dec 05 2017

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 3*a(n-4) + 3*a(n-5) - a(n-6) for n>5.

G.f.: x*(4 + 18*x + 27*x^2 + 16*x^3 + 7*x^4) / ((1 - x)^4*(1 + x + x^2)). - Colin Barker, Dec 05 2017