A047395 Numbers that are congruent to {0, 2, 6} mod 8.

0, 2, 6, 8, 10, 14, 16, 18, 22, 24, 26, 30, 32, 34, 38, 40, 42, 46, 48, 50, 54, 56, 58, 62, 64, 66, 70, 72, 74, 78, 80, 82, 86, 88, 90, 94, 96, 98, 102, 104, 106, 110, 112, 114, 118, 120, 122, 126, 128, 130, 134, 136, 138, 142, 144, 146, 150, 152, 154, 158

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

The members of this sequence together with the members of A017113 give the even numbers. - Wesley Ivan Hurt, Apr 01 2014

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).

Crossrefs

Cf. A017113, A042965, A047407, A047410, A047464.

Programs

Magma

[n : n in [0..150] | n mod 8 in [0, 2, 6]]; // Wesley Ivan Hurt, Jun 13 2016

Maple

A047395:=n->2*floor((4*n-3)/3); seq(A047395(n), n=1..100); # Wesley Ivan Hurt, Apr 01 2014

Mathematica

Table[2 Floor[(4 n - 3)/3], {n, 100}] (* Wesley Ivan Hurt, Apr 01 2014 *)
Flatten[Table[8n + {0, 2, 6}, {n, 0, 19}]] (* Alonso del Arte, Apr 11 2014 *)
LinearRecurrence[{1, 0, 1, -1}, {0, 2, 6, 8}, 100] (* Vincenzo Librandi, Jun 14 2016 *)

Formula

From R. J. Mathar, Dec 05 2011: (Start)

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

a(n) = 2 * A042965(n). (End)

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

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

a(n) = 2*(12*n-12+3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-2, a(3k-1) = 8k-6, a(3k-2) = 8k-8. (End)

a(n) = 2*(n - 1 + floor(n/3)). - Wolfdieter Lang, Sep 11 2021

Sum_{n>=2} (-1)^n/a(n) = sqrt(2)*log(sqrt(2)+2)/4 - (sqrt(2)-1)*log(2)/8. - Amiram Eldar, Dec 19 2021