A211617 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and 2w+x+y>0.

0, 3, 30, 101, 244, 479, 834, 1329, 1992, 2843, 3910, 5213, 6780, 8631, 10794, 13289, 16144, 19379, 23022, 27093, 31620, 36623, 42130, 48161, 54744, 61899, 69654, 78029, 87052, 96743, 107130, 118233, 130080, 142691, 156094, 170309, 185364, 201279, 218082

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

Formula

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

From Colin Barker, Dec 04 2017: (Start)

G.f.: x*(3 + 21*x + 17*x^2 + 7*x^3) / ((1 - x)^4*(1 + x)).

a(n) = 4*n^3 - n^2 + n for n even.

a(n) = 4*n^3 - n^2 + n - 1 for n odd.

(End)

Mathematica

t = Compile[{{u, _Integer}}, Module[{s = 0}, (Do[If[2 w + x + y > 0, s = s + 1], {w, #}, {x, #}, {y, #}] &[ Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &, Range[0, 70]]  (* A211617 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
LinearRecurrence[{3, -2, -2, 3, -1}, {0, 3, 30, 101, 244}, 36] (* Ray Chandler, Aug 02 2015 *)

Prog

(PARI) concat(0, Vec(x*(3 + 21*x + 17*x^2 + 7*x^3) / ((1 - x)^4*(1 + x)) + O(x^40))) \\ Colin Barker, Dec 04 2017

Crossrefs

Cf. A211422.

Sequence in context: A001800 A152767 A195029 * A180816 A308402 A035328

Adjacent sequences: A211614 A211615 A211616 * A211618 A211619 A211620

Keyword

nonn,easy

Author

Clark Kimberling, Apr 16 2012

Status

approved