OFFSET
1,2
COMMENTS
Complement of A047251, or "Polyrhythmic Sequence" P(2,3); the present sequence represents where the "rests" occur in a "3 against 2" polyrhythm. (See A267027 for definition and description). - Bob Selcoe, Jan 12 2016
LINKS
Bruno Berselli, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
From Bruno Berselli, Jun 24 2010: (Start)
G.f.: 2*x*(1+2*x)/((1+x)*(1-x)^2).
a(n) = a(n-1) + a(n-2) - a(n-3), a(0)=0, a(1)=2, a(2)=6.
a(n) = (6*n - (-1)^n-7)/2.
a(n) = 2*A032766(n-1). (End)
a(n) = 6*n - a(n-1) - 10 (with a(1)=0). - Vincenzo Librandi, Aug 05 2010
a(n) = 2*floor(3*n/2). - Enrique Pérez Herrero, Jul 04 2012
Sum_{n>=2} (-1)^n/a(n) = sqrt(3)*Pi/36 + log(3)/4. - Amiram Eldar, Dec 13 2021
E.g.f: 3*(x-1)*exp(x) - cosh(x) + 4. - David Lovler, Jul 11 2022
MATHEMATICA
Select[Range[0, 200], MemberQ[{0, 2}, Mod[#, 6]]&] (* or *) LinearRecurrence[ {1, 1, -1}, {0, 2, 6}, 70] (* Harvey P. Dale, Jun 15 2011 *)
PROG
(PARI) forstep(n=0, 200, [2, 4], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011
(Magma) [n: n in [0..200]|n mod 6 in {0, 2}]; // Vincenzo Librandi, Jan 12 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved