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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 16 2012
STATUS
approved