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

1,1

Comments

First differences in A010696.

Links

Table of n, a(n) for n=1..59.

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

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

Mathematica

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

Prog

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

Crossrefs

Union of A017089 and A017113.

Cf. A014848.

Sequence in context: A081887 A085344 A288225 * A107059 A160716 A071642

Adjacent sequences: A047460 A047461 A047462 * A047464 A047465 A047466

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Aug 06 2010

Status

approved