OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..5000
Melvyn B. Nathanson, On the fractional parts of roots of positive real numbers, Amer. Math. Monthly, 120 (2013), 409-429 [see p. 417].
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
From Colin Barker, Mar 13 2012
G.f.: x*(1+3*x+2*x^2+x^3)/((1-x)^2*(1+x+x^2)).
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. (End)
From Wesley Ivan Hurt, Jun 13 2016: (Start)
a(n) = (21*n-9-2*sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 7k-1, a(3k-1) = 7k-3, a(3k-2) = 7k-6. (End)
MAPLE
A047290:=n->(21*n-9-2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047290(n), n=1..100); # Wesley Ivan Hurt, Jun 13 2016
MATHEMATICA
Select[Range[0, 12000], MemberQ[{1, 4, 6}, Mod[#, 7]]&] (* Vincenzo Librandi, Apr 26 2012 *)
LinearRecurrence[{1, 0, 1, -1}, {1, 4, 6, 8}, 60] (* Harvey P. Dale, Sep 19 2014 *)
PROG
(Magma) I:=[1, 4, 6, 8]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // Vincenzo Librandi Apr 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved