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A147587 a(n) = 14*n + 7.

%I A147587 #55 Mar 19 2025 10:02:48
%S A147587 7,21,35,49,63,77,91,105,119,133,147,161,175,189,203,217,231,245,259,
%T A147587 273,287,301,315,329,343,357,371,385,399,413,427,441,455,469,483,497,
%U A147587 511,525,539,553,567,581,595,609,623,637,651,665,679,693,707,721,735
%N A147587 a(n) = 14*n + 7.
%C A147587 a(n+3) = 14*n + 49 is the sum of seven consecutive odd numbers starting with 2*n+1. - _Wesley Ivan Hurt_, Apr 11 2015
%C A147587 Numbers k such that 3^k + 1 is divisible by 547. - _Bruno Berselli_, Aug 22 2018
%C A147587 Sum of the numbers from 2*(n-1) to 2*(n+2). - _Bruno Berselli_, Oct 25 2018
%H A147587 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A147587 a(n) = a(n-1) + 14.
%F A147587 a(n) = A132355(2*n+2) - A132355(2*n+1) = 7*A005408(n).
%F A147587 a(n) = 28*n - a(n-1) for n>0, a(0)=7. - _Vincenzo Librandi_, Nov 24 2010
%F A147587 From _Wesley Ivan Hurt_, Apr 11 2015: (Start)
%F A147587 G.f.: 7*(1 + x)/(1 - x)^2.
%F A147587 a(n) = 2*a(n-1) - a(n-2). (End)
%F A147587 Sum_{n>=0} (-1)^n/a(n) = Pi/28 (A132744). - _Amiram Eldar_, Dec 13 2021
%F A147587 From _Amiram Eldar_, Nov 25 2024: (Start)
%F A147587 Product_{n>=0} (1 - (-1)^n/a(n)) = sqrt(2)*sin(3*Pi/14).
%F A147587 Product_{n>=0} (1 + (-1)^n/a(n)) = sqrt(2)*cos(3*Pi/14). (End)
%F A147587 a(n) = (n+4)^2 - (n-3)^2. - _Alexander Yutkin_, Mar 16 2025
%F A147587 E.g.f.: 7*exp(x)*(1 + 2*x). - _Stefano Spezia_, Mar 18 2025
%p A147587 A147587:=n->14*n+7: seq(A147587(n), n=0..100); # _Wesley Ivan Hurt_, Apr 11 2015
%t A147587 Range[7, 1000, 14] (* _Vladimir Joseph Stephan Orlovsky_, May 31 2011 *)
%o A147587 (Magma) [14*n+7 : n in [0..100]]; // _Wesley Ivan Hurt_, Apr 11 2015
%o A147587 (PARI) a(n)=14*n+7 \\ _Charles R Greathouse IV_, Oct 16 2015
%Y A147587 Cf. A005408, A008596, A131877, A132355, A132744.
%K A147587 nonn,easy
%O A147587 0,1
%A A147587 _Paul Curtz_, Nov 08 2008
%E A147587 More terms from _Vincenzo Librandi_, Oct 23 2009