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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 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+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]. Cf. A047251, A267027. Sequence in context: A056906 A257056 A209249 * A189933 A229488 A307699 Adjacent sequences: A047235 A047236 A047237 * A047239 A047240 A047241 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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