A047271 Numbers that are congruent to {0, 3, 5} mod 6.

0, 3, 5, 6, 9, 11, 12, 15, 17, 18, 21, 23, 24, 27, 29, 30, 33, 35, 36, 39, 41, 42, 45, 47, 48, 51, 53, 54, 57, 59, 60, 63, 65, 66, 69, 71, 72, 75, 77, 78, 81, 83, 84, 87, 89, 90, 93, 95, 96, 99, 101, 102, 105, 107, 108, 111, 113, 114, 117, 119, 120, 123, 125

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Formula

From Colin Barker, Mar 13 2012: (Start)

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

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

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

a(n) = (6*n-4+cos(2*n*Pi/3)-sqrt(3)*sin(2*Pi*n/3))/3.

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

Sum_{n>=2} (-1)^n/a(n) = log(2)/6 + log(2+sqrt(3))/(2*sqrt(3)) - Pi/12. - Amiram Eldar, Dec 14 2021

Example

G.f. = 3*x^2 + 5*x^3 + 6*x^4 + 9*x^5 + 11*x^6 + 12*x^7 +15*x^8 + 17*x^9 + ...

Maple

A047271:=n->(6*n-4+cos(2*n*Pi/3)-sqrt(3)*sin(2*Pi*n/3))/3: seq(A047271(n), n=1..100); # Wesley Ivan Hurt, Jun 13 2016

Mathematica

Select[Range[0, 120], MemberQ[{0, 3, 5}, Mod[#, 6]]&] (* Vincenzo Librandi, Apr 26 2012 *)

Prog

(Magma) I:=[0, 3, 5, 6]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // Vincenzo Librandi, Apr 26 2012

Crossrefs

Sequence in context: A053091 A367499 A324701 * A047445 A341349 A248638

Adjacent sequences: A047268 A047269 A047270 * A047272 A047273 A047274

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

G.f. corrected by Colin Barker, May 14 2012

Status

approved