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A113804
Numbers that are congruent to 4 or 10 mod 14.
11
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]
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
KEYWORD
nonn,easy
AUTHOR
Giovanni Teofilatto, Jan 22 2006
EXTENSIONS
More terms from Neven Juric, Apr 10 2008
STATUS
approved