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%I #44 Dec 25 2023 13:46:23
%S 1,5,8,12,15,19,22,26,29,33,36,40,43,47,50,54,57,61,64,68,71,75,78,82,
%T 85,89,92,96,99,103,106,110,113,117,120,124,127,131,134,138,141,145,
%U 148,152,155,159,162,166,169
%N Numbers that are congruent to {1, 5} mod 7.
%H Harvey P. Dale, <a href="/A047383/b047383.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) = ceiling((7*n+2)/2).
%F a(n) = 7*n - a(n-1) - 8 (with a(1)=1). - _Vincenzo Librandi_, Aug 05 2010
%F G.f.: x*(1+4*x+2*x^2) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Oct 08 2011
%F a(1)=1, a(2)=5, a(3)=8; for n>3, a(n) = a(n-1) + a(n-2) - a(n-3). - _Harvey P. Dale_, Dec 24 2012
%F From _Wesley Ivan Hurt_, Nov 10 2013: (Start)
%F a(n) = 4*n - floor((n-1)/2) - 3.
%F a(2*k-1) = 7*k-6, a(2*k) = 7*k-2. (End)
%F E.g.f.: 2 + ((14*x - 9)*exp(x) + exp(-x))/4. - _David Lovler_, Sep 01 2022
%p A047383:=n->((-1)^n+14*n-9)/4; seq(A047383(n), n=1..100); # _Wesley Ivan Hurt_, Nov 10 2013
%t Flatten[(#+{1,5})&/@(7Range[0,25])] (* or *) LinearRecurrence[ {1,1,-1},{1,5,8},80] (* _Harvey P. Dale_, Dec 24 2012 *)
%o (PARI) a(n)=7*n\2-2 \\ _Charles R Greathouse IV_, Jun 11 2015
%Y Cf. A001106.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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