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%I A047433 #24 Sep 08 2022 08:44:57
%S A047433 2,4,5,6,10,12,13,14,18,20,21,22,26,28,29,30,34,36,37,38,42,44,45,46,
%T A047433 50,52,53,54,58,60,61,62,66,68,69,70,74,76,77,78,82,84,85,86,90,92,93,
%U A047433 94,98,100,101,102,106,108,109,110,114,116,117,118,122,124
%N A047433 Numbers that are congruent to {2, 4, 5, 6} mod 8.
%H A047433 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047433 G.f.: x*(2+2*x+x^2+x^3+2*x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 07 2011
%F A047433 From _Wesley Ivan Hurt_, May 26 2016: (Start)
%F A047433 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047433 a(n) = (8*n-3-i^(2*n)-(2-i)*i^(-n)-(2+i)*i^n)/4 where i=sqrt(-1).
%F A047433 a(2k) = A047406(k), a(2k-1) = A047617(k). (End)
%F A047433 Sum_{n>=1} (-1)^(n+1)/a(n) = (3-sqrt(2))*Pi/16 + log(2)/4 + sqrt(2)*log(sqrt(2)-1)/8. - _Amiram Eldar_, Dec 25 2021
%p A047433 A047433:=n->(8*n-3-I^(2*n)-(2-I)*I^(-n)-(2+I)*I^n)/4: seq(A047433(n), n=1..100); # _Wesley Ivan Hurt_, May 26 2016
%t A047433 Select[Range[120], MemberQ[{2,4,5,6}, Mod[#,8]]&]  (* _Harvey P. Dale_, Mar 04 2011 *)
%o A047433 (Magma) [n : n in [0..150] | n mod 8 in [2, 4, 5, 6]]; // _Wesley Ivan Hurt_, May 26 2016
%Y A047433 Cf. A047406, A047617.
%K A047433 nonn,easy
%O A047433 1,1
%A A047433 _N. J. A. Sloane_

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