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A047593 Numbers that are congruent to {2, 3, 4, 5, 6, 7} mod 8.

%I A047593 #21 Sep 08 2022 08:44:57
%S A047593 2,3,4,5,6,7,10,11,12,13,14,15,18,19,20,21,22,23,26,27,28,29,30,31,34,
%T A047593 35,36,37,38,39,42,43,44,45,46,47,50,51,52,53,54,55,58,59,60,61,62,63,
%U A047593 66,67,68,69,70,71,74,75,76,77,78,79,82,83,84,85,86,87
%N A047593 Numbers that are congruent to {2, 3, 4, 5, 6, 7} mod 8.
%H A047593 Vincenzo Librandi, <a href="/A047593/b047593.txt">Table of n, a(n) for n = 1..1000</a>
%H A047593 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%F A047593 G.f.: x*(2+x+x^2+x^3+x^4+x^5+x^6) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - _R. J. Mathar_, Jul 10 2015
%F A047593 From _Wesley Ivan Hurt_, Jun 16 2016: (Start)
%F A047593 a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
%F A047593 a(n) = (24*n-3-3*cos(n*Pi)-4*sqrt(3)*cos((1+4*n)*Pi/6)-12*sin((1-2*n)*Pi/6))/18.
%F A047593 a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-3, a(6k-3) = 8k-4, a(6k-4) = 8k-5, a(6k-5) = 8k-6. (End)
%F A047593 Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+1)*Pi/16 + sqrt(2)*log(sqrt(2)+2)/8 - (sqrt(2)+8)*log(2)/16. - _Amiram Eldar_, Dec 28 2021
%p A047593 A047593:=n->(24*n-3-3*cos(n*Pi)-4*sqrt(3)*cos((1+4*n)*Pi/6)-12*sin((1-2*n)*Pi/6))/18: seq(A047593(n), n=1..100); # _Wesley Ivan Hurt_, Jun 16 2016
%t A047593 Select[Range[100], MemberQ[{2, 3, 4, 5, 6, 7}, Mod[#, 8]]&] (* _Vincenzo Librandi_, Jan 06 2013 *)
%o A047593 (Magma) [n: n in [1..80] | n mod 8 in [2..7]]; // _Vincenzo Librandi_, Jan 06 2013
%Y A047593 Cf. A047564, A047572.
%K A047593 nonn,easy
%O A047593 1,1
%A A047593 _N. J. A. Sloane_