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%I #36 Sep 08 2022 08:44:57
%S 0,4,6,8,12,14,16,20,22,24,28,30,32,36,38,40,44,46,48,52,54,56,60,62,
%T 64,68,70,72,76,78,80,84,86,88,92,94,96,100,102,104,108,110,112,116,
%U 118,120,124,126,128,132,134,136,140,142,144,148,150,152,156
%N Numbers that are congruent to {0, 4, 6} mod 8.
%H Vincenzo Librandi, <a href="/A047407/b047407.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F From _R. J. Mathar_, Dec 05 2011: (Start)
%F a(n) = 2*A004772(n).
%F G.f.: 2*x^2*(2+x+x^2) / ((1+x+x^2)*(x-1)^2). (End)
%F From _Wesley Ivan Hurt_, Jun 10 2016: (Start)
%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F a(n) = 2*(12*n-9-2*sqrt(3)*sin(2*n*Pi/3))/9.
%F a(3k) = 8k-2, a(3k-1) = 8k-4, a(3k-2) = 8k-8. (End)
%F a(n) = 2*(n - 1 + floor((n + 1)/3)). - _Wolfdieter Lang_, Sep 11 2021
%F Sum_{n>=2} (-1)^n/a(n) = (2-sqrt(2))*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8 - (sqrt(2)-1)*Pi/16. - _Amiram Eldar_, Dec 19 2021
%p A047407:=n->2*(12*n-9-2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047407(n), n=1..100); # _Wesley Ivan Hurt_, Jun 10 2016
%t Select[Range[0,200], MemberQ[{0,4,6}, Mod[#,8]]&] (* or *) LinearRecurrence[{1,0,1,-1}, {0,4,6,8}, 70] (* _Harvey P. Dale_, Apr 20 2016 *)
%o (Magma) [n : n in [0..160] | n mod 8 in [0, 4, 6]]; // _Vincenzo Librandi_, May 02 2016
%o (PARI) a(n)=n\3*8+[-2,0,4][n%3+1] \\ _Charles R Greathouse IV_, May 02 2016
%Y Cf. A004772, A047395, A047410, A047464.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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