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 (2,-1,2,-4,2,-1,2,-1).
FORMULA
a(n) = 2*a(n-1)-a(n-2)+2*a(n-3)-4*a(n-4)+2*a(n-5)-a(n-6)+2*a(n-7)-a(n-8).
G.f.: x*(7*x^6+23*x^5+48*x^4+66*x^3+44*x^2+24*x+4) / ((x-1)^4*(x^2+x+1)^2). - Colin Barker, Nov 17 2015
MATHEMATICA
Remove["Global`*"];
t = Compile[{{u, _Integer}},
Module[{s = 0}, (Do[If[w + 3 x + 3 y > 0,
s = s + 1], {w, #}, {x, #}, {y, #}] &[
Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
Map[t[#] &, Range[0, 60]] (* A211625 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
LinearRecurrence[{2, -1, 2, -4, 2, -1, 2, -1}, {0, 4, 32, 104, 250, 492, 845, 1349}, 36] (* Ray Chandler, Aug 02 2015 *)
PROG
(PARI) concat(0, Vec(x*(7*x^6+23*x^5+48*x^4+66*x^3+44*x^2+24*x+4)/((x-1)^4*(x^2+x+1)^2) + O(x^100))) \\ Colin Barker, Nov 17 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 17 2012
STATUS
approved