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%I #26 Sep 12 2022 08:40:30
%S 1,3,8,10,15,17,22,24,29,31,36,38,43,45,50,52,57,59,64,66,71,73,78,80,
%T 85,87,92,94,99,101,106,108,113,115,120,122,127,129,134,136,141,143,
%U 148,150,155,157,162,164,169
%N Numbers that are congruent to {1, 3} mod 7.
%C This sequence is related to A010702 by a(n) = (Sum_{i=1..n} A010702(i)) - A010702(n+1). - _Bruno Berselli_, Mar 12 2012
%H David Lovler, <a href="/A047356/b047356.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) - 10 with n > 1, a(1)=1. - _Vincenzo Librandi_, Aug 05 2010
%F From _R. J. Mathar_, Oct 08 2011: (Start)
%F a(n) = 7*n/2 - 13/4 - 3*(-1)^n/4.
%F G.f.: x*(1+2*x+4*x^2) / ( (1+x)*(x-1)^2 ). (End)
%F E.g.f.: 4 + ((14*x - 13)*exp(x) - 3*exp(-x))/4. - _David Lovler_, Sep 11 2022
%t With[{c=7 Range[0,50]},Sort[Join[c+1,c+3]]] (* or *) LinearRecurrence[ {1,1,-1},{1,3,8},100] (* _Harvey P. Dale_, May 29 2012 *)
%o (PARI) a(n) = (14*n - 13 - 3*(-1)^n)/4 \\ _David Lovler_, Sep 11 2022
%Y Cf. A010702.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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