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A211545 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and w+x+y>0. 2
0, 4, 29, 99, 238, 470, 819, 1309, 1964, 2808, 3865, 5159, 6714, 8554, 10703, 13185, 16024, 19244, 22869, 26923, 31430, 36414, 41899, 47909, 54468, 61600, 69329, 77679, 86674, 96338, 106695, 117769, 129584, 142164, 155533, 169715, 184734, 200614, 217379 (list; graph; refs; listen; history; text; internal format)
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 (4,-6,4,-1).

FORMULA

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

From Colin Barker, Dec 04 2017: (Start)

G.f.: x*(4 + 13*x + 7*x^2) / (1 - x)^4.

a(n) = (n*(3 - 3*n + 8*n^2))/2.

(End)

EXAMPLE

a(1) counts these triples: (-1,1,1), (1,-1,1), (1,1,-1), (1,1,1).

MATHEMATICA

t = Compile[{{u, _Integer}},

   Module[{s = 0}, (Do[If[w + x + y > 0, s = s + 1],

{w, #}, {x, #}, {y, #}] &[

      Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];

Map[t[#] &, Range[0, 60]]  (* A211545 *)

FindLinearRecurrence[%]

(* Peter J. C. Moses, Apr 13 2012 *)

LinearRecurrence[{4, -6, 4, -1}, {0, 4, 29, 99}, 36] (* Ray Chandler, Aug 02 2015 *)

PROG

(PARI) concat(0, Vec(x*(4 + 13*x + 7*x^2) / (1 - x)^4 + O(x^40))) \\ Colin Barker, Dec 04 2017

CROSSREFS

Cf. A211422.

Sequence in context: A288542 A024394 A199399 * A295842 A345897 A095670

Adjacent sequences:  A211542 A211543 A211544 * A211546 A211547 A211548

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 16 2012

STATUS

approved

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Last modified August 9 16:21 EDT 2022. Contains 356026 sequences. (Running on oeis4.)