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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A047245 (complement).

Programs

Magma

[2*n-2+((2*n-2) mod 3) : n in [1..100]]; // Wesley Ivan Hurt, Apr 13 2015

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 *)

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

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

Extensions

More terms from Wesley Ivan Hurt, Apr 13 2015