A047238 Numbers that are congruent to {0, 2} mod 6.

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

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