A211618 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and 2w+x+y>1.

0, 3, 24, 89, 218, 439, 772, 1245, 1878, 2699, 3728, 4993, 6514, 8319, 10428, 12869, 15662, 18835, 22408, 26409, 30858, 35783, 41204, 47149, 53638, 60699, 68352, 76625, 85538, 95119, 105388, 116373, 128094, 140579, 153848, 167929, 182842, 198615, 215268

Offset: 0

Author

Clark Kimberling, Apr 16 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,-2,-2,3,-1).

Crossrefs

Cf. A211422.

Programs

Mathematica

t = Compile[{{u, _Integer}},
   Module[{s = 0}, (Do[If[2 w + x + y > 1,
         s = s + 1], {w, #}, {x, #}, {y, #}] &[
      Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &, Range[0, 70]]  (* A211618 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
Join[{0},LinearRecurrence[{3, -2, -2, 3, -1},{3, 24, 89, 218, 439},35]] (* Ray Chandler, Aug 02 2015 *)

PARI

concat(0, Vec(x*(3 + 15*x + 23*x^2 + 5*x^3 + 2*x^4) / ((1 - x)^4*(1 + x)) + O(x^40))) \\ Colin Barker, Dec 04 2017

Formula

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

From Colin Barker, Dec 04 2017: (Start)

G.f.: x*(3 + 15*x + 23*x^2 + 5*x^3 + 2*x^4) / ((1 - x)^4*(1 + x)).

a(n) = 4*n^3 - 3*n^2 + 3*n - 2 for n>0 and even.

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

(End)