A047407 Numbers that are congruent to {0, 4, 6} mod 8.

0, 4, 6, 8, 12, 14, 16, 20, 22, 24, 28, 30, 32, 36, 38, 40, 44, 46, 48, 52, 54, 56, 60, 62, 64, 68, 70, 72, 76, 78, 80, 84, 86, 88, 92, 94, 96, 100, 102, 104, 108, 110, 112, 116, 118, 120, 124, 126, 128, 132, 134, 136, 140, 142, 144, 148, 150, 152, 156

Offset

1,2

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)

a(n) = 2*A004772(n).

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

From Wesley Ivan Hurt, Jun 10 2016: (Start)

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

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

a(3k) = 8k-2, a(3k-1) = 8k-4, a(3k-2) = 8k-8. (End)

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

Sum_{n>=2} (-1)^n/a(n) = (2-sqrt(2))*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8 - (sqrt(2)-1)*Pi/16. - Amiram Eldar, Dec 19 2021

Maple

A047407:=n->2*(12*n-9-2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047407(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0, 200], MemberQ[{0, 4, 6}, Mod[#, 8]]&] (* or *) LinearRecurrence[{1, 0, 1, -1}, {0, 4, 6, 8}, 70] (* Harvey P. Dale, Apr 20 2016 *)

Prog

(Magma) [n : n in [0..160] | n mod 8 in [0, 4, 6]]; // Vincenzo Librandi, May 02 2016
(PARI) a(n)=n\3*8+[-2, 0, 4][n%3+1] \\ Charles R Greathouse IV, May 02 2016

Crossrefs

Cf. A004772, A047395, A047410, A047464.

Sequence in context: A241124 A117247 A249722 * A090697 A359675 A225508

Adjacent sequences: A047404 A047405 A047406 * A047408 A047409 A047410

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved