A211619 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and 2w+x+y>2.

0, 1, 18, 73, 192, 395, 710, 1157, 1764, 2551, 3546, 4769, 6248, 8003, 10062, 12445, 15180, 18287, 21794, 25721, 30096, 34939, 40278, 46133, 52532, 59495, 67050, 75217, 84024, 93491, 103646, 114509, 126108, 138463, 151602, 165545, 180320, 195947, 212454

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 > 2,
         s = s + 1], {w, #}, {x, #}, {y, #}] &[
      Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &, Range[0, 70]]  (* A211619 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
Join[{0, 1},LinearRecurrence[{3, -2, -2, 3, -1},{18, 73, 192, 395, 710},34]] (* Ray Chandler, Aug 02 2015 *)

PARI

concat(0, Vec(x*(1 + 15*x + 21*x^2 + 11*x^3 - 2*x^4 + 2*x^5) / ((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>6.

From Colin Barker, Dec 04 2017: (Start)

G.f.: x*(1 + 15*x + 21*x^2 + 11*x^3 - 2*x^4 + 2*x^5) / ((1 - x)^4*(1 + x)).

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

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

(End)