A047258 Numbers that are congruent to {0, 4, 5} mod 6.

0, 4, 5, 6, 10, 11, 12, 16, 17, 18, 22, 23, 24, 28, 29, 30, 34, 35, 36, 40, 41, 42, 46, 47, 48, 52, 53, 54, 58, 59, 60, 64, 65, 66, 70, 71, 72, 76, 77, 78, 82, 83, 84, 88, 89, 90, 94, 95, 96, 100, 101, 102, 106, 107, 108, 112, 113, 114, 118, 119, 120, 124

Offset

1,2

Links

Table of n, a(n) for n=1..62.

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

Formula

G.f.: x^2*(4+x+x^2)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Apr 13 2015: (Start)

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

a(n) = 2n-2 + ((2n-2) mod 3). (End)

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

a(n) = 2*n-1-2*sin(2*n*Pi/3)/sqrt(3).

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

E.g.f.: 1 + (2*x - 1)*exp(x) - 2*sin(sqrt(3)*x/2)*(cosh(x/2) - sinh(x/2))/sqrt(3). - Ilya Gutkovskiy, Jun 14 2016

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

Maple

A047258:=n->2*n-2+((2*n-2) mod 3): seq(A047258(n), n=1..100); # Wesley Ivan Hurt, Apr 13 2015

Mathematica

Flatten[#+{0, 4, 5}&/@(6Range[0, 20])] (* Harvey P. Dale, Jul 20 2011 *)
Select[Range[0, 200], MemberQ[{0, 4, 5}, Mod[#, 6]] &] (* Vincenzo Librandi, Apr 14 2015 *)

Prog

(Magma) [2*n-2+((2*n-2) mod 3) : n in [1..100]]; // Wesley Ivan Hurt, Apr 13 2015
(PARI) concat (0, Vec(x^2*(4+x+x^2)/((1+x+x^2)*(x-1)^2) + O(x^80))) \\ Michel Marcus, Apr 14 2015

Crossrefs

Cf. A047245 (complement).

Sequence in context: A246441 A026312 A070751 * A024565 A327223 A143833

Adjacent sequences: A047255 A047256 A047257 * A047259 A047260 A047261

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Wesley Ivan Hurt, Apr 13 2015

Status

approved