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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• David Lovler, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Union of A008590 and A017089.

Cf. A030308, A042948.

Programs

Mathematica

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

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

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

Extensions

More terms from Vincenzo Librandi, Aug 06 2010