A047463 Numbers that are congruent to {2, 4} mod 8.

2, 4, 10, 12, 18, 20, 26, 28, 34, 36, 42, 44, 50, 52, 58, 60, 66, 68, 74, 76, 82, 84, 90, 92, 98, 100, 106, 108, 114, 116, 122, 124, 130, 132, 138, 140, 146, 148, 154, 156, 162, 164, 170, 172, 178, 180, 186, 188, 194, 196, 202, 204, 210, 212, 218, 220, 226, 228, 234

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

First differences in A010696.

Links

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

Crossrefs

Union of A017089 and A017113.

Cf. A014848.

Programs

Magma

[ n: n in [2..234 by 2] | n mod 8 in [2,4] ];  // Bruno Berselli, May 11 2011

Mathematica

Select[Range[250], MemberQ[{2, 4}, Mod[#, 8]] &] (* Amiram Eldar, Dec 18 2021 *)

Formula

a(n) = 8*n - a(n-1) - 10, with a(1)=2. - Vincenzo Librandi, Aug 06 2010

From Bruno Berselli, May 11 2011: (Start)

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

a(n) = 4*n-(-1)^n-3.

Sum_{i=1..n} a(i) = 2*A014848(n).

a(n) = 2*A042963(n-1). (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/16 + log(2)/8. - Amiram Eldar, Dec 18 2021

Extensions

More terms from Vincenzo Librandi, Aug 06 2010