OFFSET
1,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
a(n) = 3*floor((n+2)/3) - (n-1) mod 3. - Robert G. Wilson v and Zak Seidov, Jan 20 2006
a(n) = a(n-3)+3 = a(n-1)+a(n-3)-a(n-4). - Jaume Oliver Lafont, Dec 02 2008
G.f.: (3*x - x^2 - x^3 + 2*x^4)/(1 - x - x^3 + x^4) = x*(3 - x - x^2 + 2*x^3)/((1 + x + x^2)*(1-x)^2). - Jaume Oliver Lafont, Mar 25 2009
a(n) = 6*floor((n+2)/3) - n - 2. - Dennis P. Walsh, Aug 16 2013
a(n) = n - 2*A049347(n). - Wesley Ivan Hurt, Sep 27 2017, simplified Jun 30 2020
Sum_{n>=1} (-1)^(n+1)/a(n) = log(2). - Amiram Eldar, Jan 31 2023
MAPLE
seq(6*floor((n+2)/3)-n-2, n=1..72); # Dennis P. Walsh, Aug 16 2013
MATHEMATICA
f[n_] := Switch[ Mod[n, 3], 0, n - 2, 1, n + 2, 2, n]; Array[f, 72] (* Robert G. Wilson v, Jan 18 2006 *)
LinearRecurrence[{1, 0, 1, -1}, {3, 2, 1, 6}, 100] (* or *) CoefficientList[Series[(3 - x - x^2 + 2 x^3) / ((1 + x + x^2) (1 - x)^2), {x, 0, 80}], x] (* Vincenzo Librandi, Sep 28 2017 *)
Reverse/@Partition[Range[81], 3]//Flatten (* Harvey P. Dale, Oct 11 2020 *)
PROG
(PARI) a(n)=2+n-2*((n+2)%3); \\ Jaume Oliver Lafont, Mar 25 2009
(Magma) I:=[3, 2, 1, 6]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..80]]; // Vincenzo Librandi, Sep 28 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Parag D. Mehta (pmehta23(AT)gmail.com), Jan 16 2006
EXTENSIONS
More terms from Robert G. Wilson v, Jan 18 2006
STATUS
approved