A113802 Numbers that are congruent to {2, 12} mod 14.
2, 12, 16, 26, 30, 40, 44, 54, 58, 68, 72, 82, 86, 96, 100, 110, 114, 124, 128, 138, 142, 152, 156, 166, 170, 180, 184, 194, 198, 208, 212, 222, 226, 236, 240, 250, 254, 264, 268, 278, 282, 292, 296, 306, 310, 320, 324, 334, 338, 348, 352, 362, 366, 376, 380
Offset: 1
Programs
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Mathematica
Select[Range[400],MemberQ[{2,12},Mod[#,14]]&] (* Harvey P. Dale, Oct 30 2011 *)
Formula
a(n) = 14*n - a(n-1) - 14 (with a(1) = 2). - Vincenzo Librandi, Nov 13 2010
From Wolfdieter Lang, Dec 15 2011: (Start)
a(n) = 7*n-(7-3*(-1)^n)/2.
O.g.f.: 2*x*(1+5*x+x^2)/((1+x)*(1-x)^2).
See the contribution of Bruno Berselli under A113801. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = cot(Pi/7)*Pi/14. - Amiram Eldar, Dec 30 2021
From Amiram Eldar, Nov 25 2024: (Start)
Product_{n>=1} (1 - (-1)^n/a(n)) = cosec(Pi/7)*sin(3*Pi/14).
Product_{n>=1} (1 + (-1)^n/a(n)) = cosec(Pi/7)*sin(Pi/14). (End)