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A047238 Numbers that are congruent to {0, 2} mod 6. 14
0, 2, 6, 8, 12, 14, 18, 20, 24, 26, 30, 32, 36, 38, 42, 44, 48, 50, 54, 56, 60, 62, 66, 68, 72, 74, 78, 80, 84, 86, 90, 92, 96, 98, 102, 104, 108, 110, 114, 116, 120, 122, 126, 128, 132, 134, 138, 140, 144, 146, 150, 152, 156, 158, 162 (list; graph; refs; listen; history; text; internal format)
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
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+1) = Sum_{k>=0} A030308(n,k)*A111286(k+2). - Philippe Deléham, Oct 17 2011
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
Cf. A047270 [(6*n-(-1)^n-1)/2], A047235 [(6*n-(-1)^n-3)/2], A047241 [(6*n-(-1)^n-5)/2].
Sequence in context: A056906 A257056 A209249 * A189933 A229488 A307699
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified February 26 11:46 EST 2024. Contains 370352 sequences. (Running on oeis4.)