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A047329 Numbers that are congruent to {1, 3, 5, 6} mod 7.

%I A047329 #27 Sep 08 2022 08:44:57
%S A047329 1,3,5,6,8,10,12,13,15,17,19,20,22,24,26,27,29,31,33,34,36,38,40,41,
%T A047329 43,45,47,48,50,52,54,55,57,59,61,62,64,66,68,69,71,73,75,76,78,80,82,
%U A047329 83,85,87,89,90,92,94,96,97,99,101,103,104,106,108,110,111
%N A047329 Numbers that are congruent to {1, 3, 5, 6} mod 7.
%D A047329 Robert Fludd, Utriusque Cosmi ... Historia, Oppenheim, 1617-1619.
%H A047329 Robert Fludd, <a href="http://beinecke.library.yale.edu/dl_crosscollex/photoneg/printoneITEM.asp?pid=39002036242312&amp;iid=3624231">Page 158 of "Utriusque Cosmi"</a> in Beinecke Rare Book and Manuscript Library Photonegatives Collection.
%H A047329 Robert Fludd, <a href="http://highway55.library.yale.edu/PHOTONEGIMG/zoom/Z362/z3624231.jpg">Larger version of the same image</a>
%H A047329 Robert Fludd, <a href="http://billheidrick.com/Orpd/RFludd/">Utriusque Cosmi, Maioris scilicet et Minoris, metaphysica, physica, atque technica Historia</a>, available as ZIP or PDF download.
%H A047329 Wikipedia, <a href="http://en.wikipedia.org/wiki/Robert_Fludd">Robert Fludd</a>
%H A047329 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047329 a(n) = floor((7n-1)/4). - _Gary Detlefs_, Mar 07 2010
%F A047329 G.f.: (x*(1+2*x+2*x^2+x^3+x^4)) / ((1+x)*(x^2+1)*(x-1)^2). - _R. J. Mathar_, Oct 08 2011
%F A047329 From _Wesley Ivan Hurt_, May 21 2016: (Start)
%F A047329 a(n) = a(n-1)+a(n-4)-a(n-5) for n>5.
%F A047329 a(n) = (14n-5-i^(2n)-(1+i)*i^(-n)-(1-i)*i^n)/8 where i=sqrt(-1).
%F A047329 a(2n) = A047280(n), a(2n-1) = A047383(n). (End)
%F A047329 E.g.f.: (4 - sin(x) - cos(x) + (7*x - 2)*sinh(x) + (7*x - 3)*cosh(x))/4. - _Ilya Gutkovskiy_, May 21 2016
%p A047329 A047329:=n->floor((7*n-1)/4): seq(A047329(n), n=1..100); # _Wesley Ivan Hurt_, May 21 2016
%t A047329 Table[Floor[(7*n-1)/4], {n, 80}] (* _Wesley Ivan Hurt_, May 21 2016 *)
%t A047329 #+{1,3,5,6}&/@(7*Range[0,20])//Flatten (* _Harvey P. Dale_, Jan 07 2021 *)
%o A047329 (Haskell)
%o A047329 a047329 n = a047329_list !! (n-1)
%o A047329 a047329_list = [1, 3, 5, 6] ++ map (+ 7) a047329_list
%o A047329 -- _Reinhard Zumkeller_, Jan 07 2014
%o A047329 (Magma) [Floor((7*n-1)/4) : n in [1..100]]; // _Wesley Ivan Hurt_, May 21 2016
%Y A047329 Cf. A047280, A047383, A082977.
%K A047329 nonn,easy
%O A047329 1,2
%A A047329 _N. J. A. Sloane_
%E A047329 Fludd reference from _Brendan McKay_, May 27 2003
%E A047329 More terms from _Wesley Ivan Hurt_, May 21 2016