A047231 Numbers that are congruent to {0, 3, 4} mod 6.

0, 3, 4, 6, 9, 10, 12, 15, 16, 18, 21, 22, 24, 27, 28, 30, 33, 34, 36, 39, 40, 42, 45, 46, 48, 51, 52, 54, 57, 58, 60, 63, 64, 66, 69, 70, 72, 75, 76, 78, 81, 82, 84, 87, 88, 90, 93, 94, 96, 99, 100, 102, 105, 106, 108, 111, 112, 114, 117, 118, 120, 123, 124

Offset

1,2

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

From R. J. Mathar, Aug 05 2010: (Start)

G.f.: x^2*(3+x+2*x^2) / ( (1+x+x^2)*(x-1)^2 ).

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

a(n) = 2*n+2-(11+A061347(n+1))/3. (End)

From Wesley Ivan Hurt, Jun 13 2016: (Start)

a(n) = (6*n-5-cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/3.

a(3k) = 6k-2, a(3k-1) = 6k-3, a(3k-2) = 6k-6. (End)

Sum_{n>=2} (-1)^n/a(n) = log(2)/3 + (1-2/sqrt(3))*Pi/12. - Amiram Eldar, Dec 14 2021

Maple

A047231:=n->(6*n-5-cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/3: seq(A047231(n), n=1..100); # Wesley Ivan Hurt, Jun 13 2016

Mathematica

Select[Range[0, 600], MemberQ[{0, 3, 4}, Mod[#, 6]]&] (* Vincenzo Librandi, Jan 06 2013 *)
LinearRecurrence[{1, 0, 1, -1}, {0, 3, 4, 6}, 70] (* Harvey P. Dale, Sep 03 2017 *)

Prog

(Magma) [n: n in [0..120] | n mod 6 in [0, 3, 4]]; // Vincenzo Librandi, Jan 06 2013

Crossrefs

Cf. A061347.

Sequence in context: A288463 A189297 A350977 * A050131 A332023 A361837

Adjacent sequences: A047228 A047229 A047230 * A047232 A047233 A047234

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved