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A113803
Numbers that are congruent to {3, 11} mod 14.
7
3, 11, 17, 25, 31, 39, 45, 53, 59, 67, 73, 81, 87, 95, 101, 109, 115, 123, 129, 137, 143, 151, 157, 165, 171, 179, 185, 193, 199, 207, 213, 221, 227, 235, 241, 249, 255, 263, 269, 277, 283, 291, 297, 305, 311, 319, 325, 333, 339, 347, 353, 361, 367
OFFSET
1,1
FORMULA
a(n) = 14*n - a(n-1) - 14 (with a(1) = 3). - Vincenzo Librandi, Nov 13 2010
From Wolfdieter Lang, Dec 15 2011: (Start)
a(n) = 7*n-(7-(-1)^n)/2.
O.g.f.: x*(3+8*x+3*x^2)/((1+x)*(1-x)^2).
See the Bruno Berselli contribution under A113801. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = cot(3*Pi/14)*Pi/14. - Amiram Eldar, Dec 30 2021
MATHEMATICA
{3+#, 11+#}&/@(14*Range[0, 30])//Flatten (* Harvey P. Dale, Jun 28 2020 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Giovanni Teofilatto, Jan 22 2006
STATUS
approved