|
%I #40 Jan 08 2023 10:59:23
%S 4,10,18,24,32,38,46,52,60,66,74,80,88,94,102,108,116,122,130,136,144,
%T 150,158,164,172,178,186,192,200,206,214,220,228,234,242,248,256,262,
%U 270,276,284,290,298,304,312,318,326,332,340,346,354,360
%N Numbers that are congruent to 4 or 10 mod 14.
%C Fourth row of the 7-rowed array A113807. - _Giovanni Teofilatto_, Oct 26 2009 [crossref added by _Wolfdieter Lang_, Dec 15 2011]
%H David Lovler, <a href="/A113804/b113804.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F From _R. J. Mathar_, Aug 13 2008: (Start)
%F a(n) = 7n - ((-1)^n + 7)/2.
%F G.f.: 2x*(2 + 3x + 2x^2)/((1-x)^2*(1+x)). (End)
%F a(n) = 14*n - a(n-1) - 14 (with a(1)=4). - _Vincenzo Librandi_, Aug 01 2010
%F Sum_{n>=1} (-1)^(n+1)/a(n) = tan(3*Pi/14)*Pi/14. - _Amiram Eldar_, Dec 30 2021
%F E.g.f.: 4 + ((14*x - 7)*exp(x) - exp(-x))/2. - _David Lovler_, Sep 04 2022
%F a(n) = 2*A047385(n). - _Michel Marcus_, Sep 05 2022
%t 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 *)
%o (PARI) a(n)=7*n-((-1)^n+7)/2 \\ _Charles R Greathouse IV_, Dec 27 2011
%Y Cf. A047385, A113801, A113802, A113803, A113805, A113806, A008589, A113807.
%K nonn,easy
%O 1,1
%A _Giovanni Teofilatto_, Jan 22 2006
%E More terms from Neven Juric, Apr 10 2008
|
