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%I #27 Sep 08 2022 08:44:57
%S 2,3,4,6,10,11,12,14,18,19,20,22,26,27,28,30,34,35,36,38,42,43,44,46,
%T 50,51,52,54,58,59,60,62,66,67,68,70,74,75,76,78,82,83,84,86,90,91,92,
%U 94,98,99,100,102,106,107,108,110,114,115,116,118,122,123
%N Numbers that are congruent to {2, 3, 4, 6} mod 8.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F G.f.: x*(2+x+x^2+2*x^3+2*x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 05 2011
%F From _Wesley Ivan Hurt_, May 25 2016: (Start)
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F a(n) = (8*n-5-i^(2*n)-(1-2*i)*i^(-n)-(1+2*i)*i^n)/4 with i=sqrt(-1).
%F a(2k) = A047398(k), a(2k-1) = A047463(k). (End)
%F E.g.f.: 2 + sin(x) - cos(x)/2 + (2*x - 1)*sinh(x) + (2*x - 3/2)*cosh(x). - _Ilya Gutkovskiy_, May 25 2016
%F Sum_{n>=1} (-1)^(n+1)/a(n) = (3-sqrt(2))*Pi/16 - (sqrt(2)+4)*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8. - _Amiram Eldar_, Dec 25 2021
%p A047417:=n->(8*n-5-I^(2*n)-(1-2*I)*I^(-n)-(1+2*I)*I^n)/4: seq(A047417(n), n=1..100); # _Wesley Ivan Hurt_, May 25 2016
%t Flatten[#+{2,3,4,6}&/@(8Range[0,20])] (* _Harvey P. Dale_, Dec 20 2012 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [2, 3, 4, 6]]; // _Wesley Ivan Hurt_, May 25 2016
%Y Cf. A047398, A047463.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
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