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

1,1

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).

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A310556 A310557 A079287 * A107372 A113420 A053767

Adjacent sequences: A113801 A113802 A113803 * A113805 A113806 A113807

Keyword

nonn,easy

Author

Giovanni Teofilatto, Jan 22 2006

Extensions

More terms from Neven Juric, Apr 10 2008

Status

approved