OFFSET
1,2
COMMENTS
Numbers whose binary expansion does not end in 01.
Equals partial sums of 0 together with 2, 1, 1, 2, 1, 1, ... (repeated, that is A131534 without the first term). - Bruno Berselli, Dec 06 2016
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
G.f.: x^2*(2 + x + x^2)/((1 + x + x^2)*(x - 1)^2). - R. J. Mathar, Oct 08 2011
a(n) = floor((4*n-2)/3). - Gary Detlefs, Jan 02 2012
a(n) = n + ceiling((n-1)/3) - 1. - Arkadiusz Wesolowski, Sep 18 2012
From Ant King, Oct 19 2012: (Start)
a(n) = 4 + a(n-3).
a(n) = (12*n -9 - 3*cos(2*(n-1)*Pi/3) + sqrt(3)*sin(2*(n-1)*Pi/3))/9. (End)
a(n) = ceiling(4*(n-1)/3). - Jean-François Alcover, Mar 07 2014
Sum_{n>=2} (-1)^n/a(n) = log(sqrt(2)+2)/(2*sqrt(2)) + (2-sqrt(2))*log(2)/8 - (sqrt(2)-1)*Pi/8. - Amiram Eldar, Dec 05 2021
MAPLE
seq(seq(4*i+j, j=[0, 2, 3]), i=0..100); # Robert Israel, Sep 01 2015
MATHEMATICA
LinearRecurrence[{1, 0, 1, -1}, {0, 2, 3, 4}, 68] (* Ant King, Oct 19 2012 *)
DeleteCases[Range[0, 90], _?(Mod[#, 4]==1&)] (* Harvey P. Dale, Jun 11 2013 *)
CoefficientList[Series[x (2 + x + x^2)/((1 + x + x^2) (x - 1)^2), {x, 0, 100}], x] (* Vincenzo Librandi, Mar 08 2014 *)
PROG
(Magma) [n: n in [0..100] | not n mod 4 eq 1 ]; // Vincenzo Librandi, Mar 09 2014
(Magma) [(4*n-2) div 3: n in [1..100]]; // Bruno Berselli, Dec 06 2016
(PARI) a(n) = (4*n-2)\3; \\ Michel Marcus, Sep 03 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Corrected by Michael Somos, Jun 08 2000
STATUS
approved