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

1,2

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).

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A166447 A075332 A141105 * A349166 A284794 A187692

Adjacent sequences: A047392 A047393 A047394 * A047396 A047397 A047398

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved