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%I #26 Sep 08 2022 08:44:57
%S 0,1,2,3,4,7,8,9,10,11,12,15,16,17,18,19,20,23,24,25,26,27,28,31,32,
%T 33,34,35,36,39,40,41,42,43,44,47,48,49,50,51,52,55,56,57,58,59,60,63,
%U 64,65,66,67,68,71,72,73,74,75,76,79,80,81,82,83,84,87,88
%N Numbers that are congruent to {0, 1, 2, 3, 4, 7} mod 8.
%H G. C. Greubel, <a href="/A047549/b047549.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%F From _Chai Wah Wu_, May 29 2016: (Start)
%F a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
%F G.f.: x^2*(x^5 + 3*x^4 + x^3 + x^2 + x + 1)/(x^7 - x^6 - x + 1). (End)
%F From _Wesley Ivan Hurt_, Jun 16 2016: (Start)
%F a(n) = (24*n-33+3*cos(n*Pi)+4*sqrt(3)*cos((1-4*n)*Pi/6)+12*sin((1+
%F 2*n)*Pi/6))/18.
%F a(6k) = 8k-1, a(6k-1) = 8k-4, a(6k-2) = 8k-5, a(6k-3) = 8k-6, a(6k-4) = 8k-7, a(6k-5) = 8k-8. (End)
%F Sum_{n>=2} (-1)^n/a(n) = (14-sqrt(2))*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8 - (2-sqrt(2))*Pi/16. - _Amiram Eldar_, Dec 26 2021
%p A047549:=n->(24*n-33+3*cos(n*Pi)+4*sqrt(3)*cos((1-4*n)*Pi/6)+12*sin((1+
%p 2*n)*Pi/6))/18: seq(A047549(n), n=1..100); # _Wesley Ivan Hurt_, Jun 16 2016
%t LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 4, 7, 8}, 50] (* _G. C. Greubel_, May 29 2016 *)
%o (Magma) [n : n in [0..100] | n mod 8 in [0..4] cat [7]]; // _Wesley Ivan Hurt_, May 29 2016
%Y Cf. A047420, A047602.
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_
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