A211627 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and w+5x+5y>0.

0, 4, 32, 108, 256, 492, 854, 1360, 2034, 2900, 3965, 5285, 6869, 8741, 10925, 13419, 16297, 19559, 23229, 27331, 31854, 36890, 42430, 48498, 55118, 62270, 70064, 78482, 87548, 97286, 107667, 118819, 130715, 143379, 156835, 171045, 186155, 202129, 218991

Offset

0,2

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,-1,0,0,2,-4,2,0,0,-1,2,-1).

Formula

a(n) = 2*a(n-1) - a(n-2) + 2*a(n-5) - 4*a(n-6) + 2*a(n-7) - a(n-10) + 2*a(n-11) - a(n-12) for n>11.

G.f.: x*(4 + 24*x + 48*x^2 + 72*x^3 + 88*x^4 + 118*x^5 + 96*x^6 + 72*x^7 + 48*x^8 + 23*x^9 + 7*x^10) / ((1 - x)^4*(1 + x + x^2 + x^3 + x^4)^2). - Colin Barker, Dec 05 2017

Mathematica

t = Compile[{{u, _Integer}},
   Module[{s = 0}, (Do[If[w + 5 x + 5 y > 0,
         s = s + 1], {w, #}, {x, #}, {y, #}] &[
      Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &, Range[0, 60]]  (* A211627 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
LinearRecurrence[{2, -1, 0, 0, 2, -4, 2, 0, 0, -1, 2, -1}, {0, 4, 32, 108, 256, 492, 854, 1360, 2034, 2900, 3965, 5285}, 36] (* Ray Chandler, Aug 02 2015 *)

Prog

(PARI) concat(0, Vec(x*(4 + 24*x + 48*x^2 + 72*x^3 + 88*x^4 + 118*x^5 + 96*x^6 + 72*x^7 + 48*x^8 + 23*x^9 + 7*x^10) / ((1 - x)^4*(1 + x + x^2 + x^3 + x^4)^2) + O(x^40))) \\ Colin Barker, Dec 05 2017

Crossrefs

Cf. A211422.

Sequence in context: A211625 A211630 A211626 * A033430 A267668 A338322

Adjacent sequences: A211624 A211625 A211626 * A211628 A211629 A211630

Keyword

nonn,easy

Author

Clark Kimberling, Apr 17 2012

Status

approved