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A047422 Numbers that are congruent to {1, 2, 3, 4, 5, 6} mod 8.

%I A047422 #19 Sep 08 2022 08:44:57
%S A047422 1,2,3,4,5,6,9,10,11,12,13,14,17,18,19,20,21,22,25,26,27,28,29,30,33,
%T A047422 34,35,36,37,38,41,42,43,44,45,46,49,50,51,52,53,54,57,58,59,60,61,62,
%U A047422 65,66,67,68,69,70,73,74,75,76,77,78,81,82,83,84,85,86
%N A047422 Numbers that are congruent to {1, 2, 3, 4, 5, 6} mod 8.
%H A047422 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%F A047422 G.f.: x*(1+x+x^2+x^3+x^4+x^5+2*x^6) / ((1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2). - _R. J. Mathar_, Dec 05 2011
%F A047422 From _Wesley Ivan Hurt_, Jun 16 2016: (Start)
%F A047422 a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
%F A047422 a(n) = (24*n-21-3*cos(n*Pi)-4*sqrt(3)*cos((1+4*n)*Pi/6)-12*sin((1-2*n)*Pi/6))/18.
%F A047422 a(6k) = 8k-2, a(6k-1) = 8k-3, a(6k-2) = 8k-4, a(6k-3) = 8k-5, a(6k-4) = 8k-6, a(6k-5) = 8k-7. (End)
%F A047422 Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+1)*Pi/16 + log(2)/2 + sqrt(2)*log(3-2*sqrt(2))/16. - _Amiram Eldar_, Dec 28 2021
%p A047422 A047422:=n->(24*n-21-3*cos(n*Pi)-4*sqrt(3)*cos((1+4*n)*Pi/6)-12*sin((1-2*n)*Pi/6))/18: seq(A047422(n), n=1..100); # _Wesley Ivan Hurt_, Jun 16 2016
%t A047422 Select[Range[0, 100], MemberQ[{1, 2, 3, 4, 5, 6}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 16 2016 *)
%o A047422 (Magma) [n : n in [0..100] | n mod 8 in [1..6]]; // _Wesley Ivan Hurt_, Jun 16 2016
%Y A047422 Cf. A047504, A047519.
%K A047422 nonn,easy
%O A047422 1,2
%A A047422 _N. J. A. Sloane_