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A047447 Numbers that are congruent to {2, 3, 5, 6} mod 8.

%I A047447 #20 Sep 08 2022 08:44:57
%S A047447 2,3,5,6,10,11,13,14,18,19,21,22,26,27,29,30,34,35,37,38,42,43,45,46,
%T A047447 50,51,53,54,58,59,61,62,66,67,69,70,74,75,77,78,82,83,85,86,90,91,93,
%U A047447 94,98,99,101,102,106,107,109,110,114,115,117,118,122,123
%N A047447 Numbers that are congruent to {2, 3, 5, 6} mod 8.
%H A047447 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047447 G.f.: x*(2+x+2*x^2+x^3+2*x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 07 2011
%F A047447 From _Wesley Ivan Hurt_, May 26 2016: (Start)
%F A047447 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047447 a(n) = (1+i)*(4*n-4*n*i+2*i-2-(1-i)*i^(2*n)+i^(1-n)-i^n)/4 where i=sqrt(-1).
%F A047447 a(2k) = A047398(k), a(2k-1) = A047617(k). (End)
%F A047447 E.g.f.: (4 + sin(x) - cos(x) + (4*x - 1)*sinh(x) + (4*x - 3)*cosh(x))/2. - _Ilya Gutkovskiy_, May 27 2016
%F A047447 Sum_{n>=1} (-1)^(n+1)/a(n) = (2-sqrt(2))*Pi/8. - _Amiram Eldar_, Dec 25 2021
%p A047447 A047447:=n->(1+I)*(4*n-4*n*I+2*I-2-(1-I)*I^(2*n)+I^(1-n)-I^n)/4: seq(A047447(n), n=1..100); # _Wesley Ivan Hurt_, May 26 2016
%t A047447 Table[(1+I)*(4n-4*n*I+2*I-2-(1-I)*I^(2n)+I^(1-n)-I^n)/4, {n, 80}] (* _Wesley Ivan Hurt_, May 26 2016 *)
%o A047447 (Magma) [n : n in [0..150] | n mod 8 in [2, 3, 5, 6]]; // _Wesley Ivan Hurt_, May 26 2016
%Y A047447 Cf. A047398, A047617.
%K A047447 nonn,easy
%O A047447 1,1
%A A047447 _N. J. A. Sloane_