A211630 Number of ordered triples (w,x,y) with all terms in {-n, ..., -1, 1, ..., n} and 5w + x + y > 0.

0, 4, 32, 106, 252, 495, 855, 1359, 2029, 2891, 3970, 5286, 6866, 8732, 10910, 13425, 16297, 19553, 23215, 27309, 31860, 36888, 42420, 48478, 55088, 62275, 70059, 78467, 87521, 97247, 107670, 118810, 130694, 143344, 156786, 171045, 186141, 202101, 218947

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,-3,1,0,1,-3,3,-1).

Crossrefs

Cf. A211422.

Programs

Mathematica

t = Compile[{{u, _Integer}},
   Module[{s = 0}, (Do[If[5 w + x + y > 0,
         s = s + 1], {w, #}, {x, #}, {y, #}] &[
      Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &, Range[0, 60]]  (* A211630 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
LinearRecurrence[{3, -3, 1, 0, 1, -3, 3, -1},{0, 4, 32, 106, 252, 495, 855, 1359},36] (* Ray Chandler, Aug 02 2015 *)

PARI

concat(0, Vec(x*(4 + 20*x + 22*x^2 + 26*x^3 + 25*x^4 + 16*x^5 + 7*x^6) / ((1 - x)^4*(1 + x + x^2 + x^3 + x^4)) + O(x^40))) \\ Colin Barker, Dec 05 2017

Formula

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

G.f.: x*(4 + 20*x + 22*x^2 + 26*x^3 + 25*x^4 + 16*x^5 + 7*x^6) / ((1 - x)^4*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Dec 05 2017