%I #35 Sep 15 2022 01:07:17

%S 3,6,10,13,17,20,24,27,31,34,38,41,45,48,52,55,59,62,66,69,73,76,80,

%T 83,87,90,94,97,101,104,108,111,115,118,122,125,129,132,136,139,143,

%U 146,150,153,157,160,164,167,171,174,178,181,185,188,192,195,199,202

%N Numbers that are congruent to {3, 6} mod 7.

%H David Lovler, <a href="/A047280/b047280.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 a(n) = 7*n - a(n-1) - 5 with n > 1, a(1)=3. - _Vincenzo Librandi_, Aug 05 2010

%F G.f.: x*(3 + 3*x + x^2) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Oct 25 2011

%F a(n) = 3*n + ceiling(n/2) - 1. - _Arkadiusz Wesolowski_, Sep 20 2012

%F a(n) = 4n - 1 - floor(n/2). - _Wesley Ivan Hurt_, Oct 16 2013

%F E.g.f.: 1 + ((14*x - 3)*exp(x) - exp(-x))/4. - _David Lovler_, Sep 14 2022

%p A047280:=n->4*n-1-floor(n/2); seq(A047280(k),k=1..100); # _Wesley Ivan Hurt_, Oct 16 2013

%t Flatten[#+{3,6}&/@(7Range[0,30])] (* _Harvey P. Dale_, Jan 11 2011 *)

%o (PARI) a(n) = 4*n - 1 - floor(n/2) \\ _David Lovler_, Sep 14 2022

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_