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%I #35 Feb 17 2024 10:34:13
%S 3,5,10,12,17,19,24,26,31,33,38,40,45,47,52,54,59,61,66,68,73,75,80,
%T 82,87,89,94,96,101,103,108,110,115,117,122,124,129,131,136,138,143,
%U 145,150,152,157,159,164,166,171
%N Numbers that are congruent to {3, 5} mod 7.
%H David Lovler, <a href="/A047389/b047389.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) - 6, n > 1. - _Vincenzo Librandi_, Aug 05 2010
%F From _Bruno Berselli_, Sep 08 2010: (Start)
%F G.f.: x*(3 + 2*x + 2*x^2)/((1+x)*(1-x)^2).
%F a(n) - a(n-1) - a(n-2) + a(n-3) = 0 for n > 3.
%F a(n) = (14*n - 5 - 3*(-1)^n)/4. (End)
%F E.g.f.: 2 + ((14*x - 5)*exp(x) - 3*exp(-x))/4. - _David Lovler_, Sep 13 2022
%t #+{3,5}&/@(7*Range[0,30])//Flatten (* _Harvey P. Dale_, Oct 10 2019 *)
%o (PARI) a(n) = (14*n - 5 - 3*(-1)^n)/4 \\ _David Lovler_, Sep 13 2022
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
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