A113804 Numbers that are congruent to 4 or 10 mod 14.

4, 10, 18, 24, 32, 38, 46, 52, 60, 66, 74, 80, 88, 94, 102, 108, 116, 122, 130, 136, 144, 150, 158, 164, 172, 178, 186, 192, 200, 206, 214, 220, 228, 234, 242, 248, 256, 262, 270, 276, 284, 290, 298, 304, 312, 318, 326, 332, 340, 346, 354, 360

Offset: 1

Author

Giovanni Teofilatto, Jan 22 2006

Keywords

• nonn
• easy

Comments

Fourth row of the 7-rowed array A113807. - Giovanni Teofilatto, Oct 26 2009 [crossref added by Wolfdieter Lang, Dec 15 2011]

Links

• David Lovler, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A047385, A113801, A113802, A113803, A113805, A113806, A008589, A113807.

Programs

Mathematica

Select[Range[2,400,2],MemberQ[{4,10},Mod[#,14]]&] (* or *) LinearRecurrence[{1,1,-1},{4,10,18},60] (* Harvey P. Dale, Jan 08 2023 *)

PARI

a(n)=7*n-((-1)^n+7)/2 \\ Charles R Greathouse IV, Dec 27 2011

Formula

From R. J. Mathar, Aug 13 2008: (Start)

a(n) = 7n - ((-1)^n + 7)/2.

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

a(n) = 14*n - a(n-1) - 14 (with a(1)=4). - Vincenzo Librandi, Aug 01 2010

Sum_{n>=1} (-1)^(n+1)/a(n) = tan(3*Pi/14)*Pi/14. - Amiram Eldar, Dec 30 2021

E.g.f.: 4 + ((14*x - 7)*exp(x) - exp(-x))/2. - David Lovler, Sep 04 2022

a(n) = 2*A047385(n). - Michel Marcus, Sep 05 2022

From Amiram Eldar, Nov 25 2024: (Start)

Product_{n>=1} (1 - (-1)^n/a(n)) = cosec(Pi/7)/2.

Product_{n>=1} (1 + (-1)^n/a(n)) = tan(3*Pi/14). (End)

Extensions

More terms from Neven Juric, Apr 10 2008