A047464 Numbers that are congruent to {0, 2, 4} mod 8.

0, 2, 4, 8, 10, 12, 16, 18, 20, 24, 26, 28, 32, 34, 36, 40, 42, 44, 48, 50, 52, 56, 58, 60, 64, 66, 68, 72, 74, 76, 80, 82, 84, 88, 90, 92, 96, 98, 100, 104, 106, 108, 112, 114, 116, 120, 122, 124, 128, 130, 132, 136, 138, 140, 144, 146, 148, 152, 154, 156

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• changed

Links

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

Crossrefs

Cf. A004773, A047395, A047407, A047410.

Programs

Magma

[n : n in [0..150] | n mod 8 in [0, 2, 4]]; // Wesley Ivan Hurt, Jun 10 2016

Maple

A047464:=n->2*(12*n-15-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047464(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Flatten[#+{0,2,4}&/@(8Range[0,20])] (* or *) LinearRecurrence[{1,0,1,-1}, {0,2,4,8}, 80] (* Harvey P. Dale, May 04 2013 *)

Formula

a(n) = 2*floor((n-1)/3)+2*n-2. - Gary Detlefs, Mar 18 2010

a(n) = 2*A004773(n-1). G.f.: 2*x^2*(1+x+2*x^2)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Mar 29 2010

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-15-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.

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

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

a(n) = A047217(n)+n-1. - R. J. Mathar, Aug 25 2025