A047467 Numbers that are congruent to {0, 2} mod 8.

0, 2, 8, 10, 16, 18, 24, 26, 32, 34, 40, 42, 48, 50, 56, 58, 64, 66, 72, 74, 80, 82, 88, 90, 96, 98, 104, 106, 112, 114, 120, 122, 128, 130, 136, 138, 144, 146, 152, 154, 160, 162, 168, 170, 176, 178, 184, 186, 192, 194, 200, 202, 208, 210, 216, 218, 224, 226, 232

Offset

1,2

Links

David Lovler, Table of n, a(n) for n = 1..10000

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

Formula

From R. J. Mathar, Sep 19 2008: (Start)

a(n) = 4*n - 5 - (-1)^n = 2*A042948(n-1).

G.f.: 2*x^2*(1+3x)/((1-x)^2*(1+x)). (End)

a(n) = 8*n - a(n-1) - 14 with a(1)=0. - Vincenzo Librandi, Aug 06 2010

a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=2 and b(k)=2^(k+2)for k > 0. - Philippe Deléham, Oct 17 2011

a(n) = floor((8/3)*floor(3*n/2)). - Clark Kimberling, Jul 04 2012

Sum_{n>=2} (-1)^n/a(n) = Pi/16 + 3*log(2)/8. - Amiram Eldar, Dec 18 2021

E.g.f.: 6 + (4*x - 5)*exp(x) - exp(-x). - David Lovler, Jul 22 2022

Mathematica

{#, #+2}&/@(8*Range[0, 30])//Flatten (* or *) LinearRecurrence[{1, 1, -1}, {0, 2, 8}, 60] (* Harvey P. Dale, Nov 30 2019 *)

Prog

(PARI) forstep(n=0, 200, [2, 6], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011
(PARI) a(n) = 4*n - 5 - (-1)^n; \\ David Lovler, Jul 25 2022

Crossrefs

Union of A008590 and A017089.

Cf. A030308, A042948.

Sequence in context: A329952 A073886 A079930 * A079599 A126002 A110913

Adjacent sequences: A047464 A047465 A047466 * A047468 A047469 A047470

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Aug 06 2010

Status

approved