A047420 Numbers that are congruent to {0, 1, 2, 3, 4, 6} mod 8.

0, 1, 2, 3, 4, 6, 8, 9, 10, 11, 12, 14, 16, 17, 18, 19, 20, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 40, 41, 42, 43, 44, 46, 48, 49, 50, 51, 52, 54, 56, 57, 58, 59, 60, 62, 64, 65, 66, 67, 68, 70, 72, 73, 74, 75, 76, 78, 80, 81, 82, 83, 84, 86, 88

Offset

1,3

Comments

The product of any two terms belongs to the sequence and therefore also a(n)^2, a(n)^3, a(n)^4, etc. - Bruno Berselli, Nov 28 2012

Links

Table of n, a(n) for n=1..67.

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-1).

Formula

a(n+1) = 6*floor(n/3)+(n mod 3). - Gary Detlefs, Mar 09 2010

G.f.: x^2*(1+x^2+2*x^4) / ( (1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Dec 05 2011

From Wesley Ivan Hurt, Jun 15 2016: (Start)

a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-2*a(n-4)+2*a(n-5)-a(n-6) for n>6.

a(n) = (12*n-18+sqrt(3)*(3*sin(n*Pi/3)+sin(2*n*Pi/3)))/9.

a(6k) = 8k-2, a(6k-1) = 8k-4, a(6k-2) = 8k-5, a(6k-3) = 8k-6, a(6k-4) = 8k-7, a(6k-5) = 8k-8. (End)

Sum_{n>=2} (-1)^n/a(n) = (sqrt(2)-1)*Pi/8 + 3*log(2)/4. - Amiram Eldar, Dec 26 2021

Maple

A047420:=n->(12*n-18+sqrt(3)*(3*sin(n*Pi/3)+sin(2*n*Pi/3)))/9: seq(A047420(n), n=1..100); # Wesley Ivan Hurt, Jun 15 2016

Mathematica

Select[Range[0, 100], MemberQ[{0, 1, 2, 3, 4, 6}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 15 2016 *)
LinearRecurrence[{2, -2, 2, -2, 2, -1}, {0, 1, 2, 3, 4, 6}, 70] (* Harvey P. Dale, Aug 11 2021 *)

Prog

(Magma) [n : n in [0..100] | n mod 8 in [0..4] cat [6]]; // Wesley Ivan Hurt, Jun 15 2016

Crossrefs

Cf. A047549, A047602.

Sequence in context: A039147 A039107 A317544 * A039075 A050078 A075449

Adjacent sequences: A047417 A047418 A047419 * A047421 A047422 A047423

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved