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%I #34 Dec 25 2023 13:45:48
%S 0,3,4,5,6,7,8,11,12,13,14,15,16,19,20,21,22,23,24,27,28,29,30,31,32,
%T 35,36,37,38,39,40,43,44,45,46,47,48,51,52,53,54,55,56,59,60,61,62,63,
%U 64,67,68,69,70,71,72,75,76,77,78,79,80,83,84,85,86,87
%N Numbers that are congruent to {0, 3, 4, 5, 6, 7} mod 8.
%H G. C. Greubel, <a href="/A047563/b047563.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 + x^4 + x^3 + x^2 + x + 3)/(x^7 - x^6 - x + 1). (End)
%F From _Wesley Ivan Hurt_, Jun 16 2016: (Start)
%F a(n) = (24*n-9+3*cos(n*Pi)-12*cos(n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/18.
%F 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-8. (End)
%F Sum_{n>=2} (-1)^n/a(n) = 7*log(2)/8 + sqrt(2)*log(3-2*sqrt(2))/16 - sqrt(2)*Pi/16. - _Amiram Eldar_, Dec 27 2021
%p A047563:=n->(24*n-9+3*cos(n*Pi)-12*cos(n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/18: seq(A047563(n), n=1..100); # _Wesley Ivan Hurt_, Jun 16 2016
%t LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 3, 4, 5, 6, 7, 8}, 50] (* _G. C. Greubel_, May 29 2016 *)
%o (Magma) [n : n in [0..100] | n mod 8 in [0] cat [3..7]]; // _Wesley Ivan Hurt_, May 29 2016
%Y Cf. A047571.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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