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A047478 Numbers that are congruent to {1, 5, 7} mod 8.

%I A047478 #23 Sep 08 2022 08:44:57
%S A047478 1,5,7,9,13,15,17,21,23,25,29,31,33,37,39,41,45,47,49,53,55,57,61,63,
%T A047478 65,69,71,73,77,79,81,85,87,89,93,95,97,101,103,105,109,111,113,117,
%U A047478 119,121,125,127,129,133,135,137,141,143,145,149,151,153,157,159
%N A047478 Numbers that are congruent to {1, 5, 7} mod 8.
%H A047478 Vincenzo Librandi, <a href="/A047478/b047478.txt">Table of n, a(n) for n = 1..1000</a>
%H A047478 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A047478 G.f.: x*(1+4*x+2*x^2+x^3)/((1-x)^2*(1+x+x^2)). [_Colin Barker_, May 14 2012]
%F A047478 a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. - _Vincenzo Librandi_, May 16 2012
%F A047478 From _Wesley Ivan Hurt_, Jun 10 2016: (Start)
%F A047478 a(n) = (24*n-9-4*sqrt(3)*sin(2*n*Pi/3))/9.
%F A047478 a(3k) = 8k-1, a(3k-1) = 8k-3, a(3k-2) = 8k-7. (End)
%F A047478 a(n) = 2*(n + floor((n+1)/3)) - 1. - _Wolfdieter Lang_, Sep 11 2021
%p A047478 A047478:=n->(24*n-9-4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047478(n), n=1..100); # _Wesley Ivan Hurt_, Jun 10 2016
%t A047478 Select[Range[0,300], MemberQ[{1,5,7}, Mod[#,8]]&] (* _Vincenzo Librandi_, May 16 2012 *)
%o A047478 (Magma) I:=[1, 5, 7, 9]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // _Vincenzo Librandi_, May 16 2012
%Y A047478 Cf. A047484, A047529, A047623.
%K A047478 nonn,easy
%O A047478 1,2
%A A047478 _N. J. A. Sloane_