A047267 Numbers that are congruent to {0, 2, 5} mod 6.

0, 2, 5, 6, 8, 11, 12, 14, 17, 18, 20, 23, 24, 26, 29, 30, 32, 35, 36, 38, 41, 42, 44, 47, 48, 50, 53, 54, 56, 59, 60, 62, 65, 66, 68, 71, 72, 74, 77, 78, 80, 83, 84, 86, 89, 90, 92, 95, 96, 98, 101, 102, 104, 107, 108, 110, 113, 114, 116, 119, 120, 122, 125

Offset

1,2

Links

Table of n, a(n) for n=1..63.

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

Formula

a(n) = 3*n-3*floor(n/3)-(n^2 mod 3), with offset 0. - Gary Detlefs, Mar 19 2010

G.f.: x^2*(x+2)*(1+x) / ((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011

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

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

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

a(3k) = 6k-1, a(3k-1) = 6k-4, a(3k-2) = 6k-6. (End)

E.g.f.: (3 + (6*x - 5)*exp(x) + 2*cos(sqrt(3)*x/2)*(cosh(x/2) - sinh(x/2)))/3. - Ilya Gutkovskiy, Jun 14 2016

Sum_{n>=2} (-1)^n/a(n) = log(2)/3 + log(2+sqrt(3))/(2*sqrt(3)) - (3-sqrt(3))*Pi/18. - Amiram Eldar, Dec 14 2021

Maple

seq(3*n-3*floor(n/3)-(n^2 mod 3), n=0..54); # Gary Detlefs, Mar 19 2010

Mathematica

Select[Range[0, 110], MemberQ[{0, 2, 5}, Mod[#, 6]]&] (* or *) LinearRecurrence[{1, 0, 1, -1}, {0, 2, 5, 6}, 60] (* Harvey P. Dale, Aug 31 2015 *)

Prog

(Magma) [n : n in [0..150] | n mod 6 in [0, 2, 5]]; // Wesley Ivan Hurt, Jun 13 2016

Crossrefs

Cf. A011655. [Gary Detlefs, Mar 19 2010]

Sequence in context: A108857 A132142 A045751 * A058591 A247062 A059009

Adjacent sequences: A047264 A047265 A047266 * A047268 A047269 A047270

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved