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%I #27 Sep 08 2022 08:44:57
%S 0,2,4,5,6,7,8,10,12,13,14,15,16,18,20,21,22,23,24,26,28,29,30,31,32,
%T 34,36,37,38,39,40,42,44,45,46,47,48,50,52,53,54,55,56,58,60,61,62,63,
%U 64,66,68,69,70,71,72,74,76,77,78,79,80,82,84,85,86,87,88,90
%N Numbers that are congruent to {0, 2, 4, 5, 6, 7} mod 8.
%H G. C. Greubel, <a href="/A047571/b047571.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-2,2,-1).
%F From _Chai Wah Wu_, May 30 2016: (Start)
%F a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-2*a(n-4)+2*a(n-5)-a(n-6) for n>6.
%F G.f.: x^2*(x^4 + x^2 + 2)/((x - 1)^2*(x^2 - x + 1)*(x^2 + x + 1)). (End)
%F a(n) = (8*n - 2*sqrt(3)*sin(Pi*(n+1)/3) + 2*sin(2*Pi*(n+1)/3)/sqrt(3) - 4)/6. - _Ilya Gutkovskiy_, May 30 2016
%F a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-3, a(6k-3) = 8k-4, a(6k-4) = 8k-6, a(6k-5) = 8k-8. - _Wesley Ivan Hurt_, Jun 16 2016
%F Sum_{n>=2} (-1)^n/a(n) = 3*log(2)/4 - (sqrt(2)-1)*Pi/8. - _Amiram Eldar_, Dec 27 2021
%p A047571:=n->(8*n-2*sqrt(3)*sin(Pi*(n+1)/3)+2*sin(2*Pi*(n+1)/3)/sqrt(3)-4)/6: seq(A047571(n), n=1..100); # _Wesley Ivan Hurt_, Jun 16 2016
%t LinearRecurrence[{2, -2, 2, -2, 2, -1}, {0, 2, 4, 5, 6, 7} , 50] (* _G. C. Greubel_, May 30 2016 *)
%o (Magma) [n: n in [0..200] | n mod 8 in [0,2,4,5,6,7]]; // _Vincenzo Librandi_, May 30 2016
%Y Cf. A047587, A047563.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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