A211616 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and -2<=w+x+y<=2.

0, 6, 42, 102, 192, 312, 462, 642, 852, 1092, 1362, 1662, 1992, 2352, 2742, 3162, 3612, 4092, 4602, 5142, 5712, 6312, 6942, 7602, 8292, 9012, 9762, 10542, 11352, 12192, 13062, 13962, 14892, 15852, 16842, 17862, 18912, 19992, 21102, 22242, 23412, 24612, 25842

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,-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]]  (* A211616 *)
%/6                        (* integers *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
Join[{0, 6},LinearRecurrence[{3, -3, 1},{42, 102, 192},38]] (* Ray Chandler, Aug 02 2015 *)

PARI

concat(0, Vec(6*x*(1 + 4*x - x^2 + x^3) / (1 - x)^3 + O(x^40))) \\ Colin Barker, Dec 04 2017

Formula

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

From Colin Barker, Dec 04 2017: (Start)

G.f.: 6*x*(1 + 4*x - x^2 + x^3) / (1 - x)^3.

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

(End)