A211615 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and -1<=w+x+y<=1.

0, 6, 24, 60, 114, 186, 276, 384, 510, 654, 816, 996, 1194, 1410, 1644, 1896, 2166, 2454, 2760, 3084, 3426, 3786, 4164, 4560, 4974, 5406, 5856, 6324, 6810, 7314, 7836, 8376, 8934, 9510, 10104, 10716, 11346, 11994, 12660, 13344, 14046

Offset: 0

Author

Clark Kimberling, Apr 16 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A211422.

Links

• 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[-1 <= w + x + y <= 1, s = s + 1], {w, #}, {x, #}, {y, #}] &[Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &,  Range[0, 70]]  (* A211615 *)
%/6  (* A005448 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
Join[{0},LinearRecurrence[{3, -3, 1},{6, 24, 60},40]] (* Ray Chandler, Aug 02 2015 *)

Formula

a(n)= 6*A005448(n).

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

a(n) = 6-9*n+9*n^2 for n>0. G.f.: 6*x*(1+x+x^2)/(1-x)^3. [Colin Barker, Sep 09 2012]