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%I #26 Sep 12 2022 08:40:55
%S 2,3,9,10,16,17,23,24,30,31,37,38,44,45,51,52,58,59,65,66,72,73,79,80,
%T 86,87,93,94,100,101,107,108,114,115,121,122,128,129,135,136,142,143,
%U 149,150,156,157,163,164,170
%N Numbers that are congruent to {2, 3} mod 7.
%H Michael De Vlieger, <a href="/A047358/b047358.txt">Table of n, a(n) for n = 1..10000</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) - 9, n > 1. - _Vincenzo Librandi_, Aug 05 2010
%F G.f.: x*(2+x+4*x^2) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Dec 04 2011
%F E.g.f.: 4 + ((14*x - 11)*exp(x) - 5*exp(-x))/4. - _David Lovler_, Sep 11 2022
%t Select[Range@ 170, MemberQ[{2, 3}, Mod[#, 7]] &] (* or *)
%t Fold[Append[#1, 7 #2 - Last@ #1 - 9] &, {2}, Range[2, 49]] (* or *)
%t Rest@ CoefficientList[Series[x (2 + x + 4 x^2)/((1 + x) (x - 1)^2), {x, 0, 49}], x] (* _Michael De Vlieger_, Jan 12 2018 *)
%K nonn
%O 1,1
%A _N. J. A. Sloane_
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