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A047495 Numbers that are congruent to {2, 4, 5, 7} mod 8.

%I A047495 #18 Sep 08 2022 08:44:57
%S A047495 2,4,5,7,10,12,13,15,18,20,21,23,26,28,29,31,34,36,37,39,42,44,45,47,
%T A047495 50,52,53,55,58,60,61,63,66,68,69,71,74,76,77,79,82,84,85,87,90,92,93,
%U A047495 95,98,100,101,103,106,108,109,111,114,116,117,119,122,124
%N A047495 Numbers that are congruent to {2, 4, 5, 7} mod 8.
%H A047495 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-1).
%F A047495 G.f.: x*(2+x^2+x^3) / ( (x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Nov 06 2015
%F A047495 From _Wesley Ivan Hurt_, May 27 2016: (Start)
%F A047495 a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.
%F A047495 a(n) = (1+i)*(4*n-4*n*i+i-1+i^(1-n)-i^n)/4 where i=sqrt(-1).
%F A047495 a(2k) = A047535(k), a(2k-1) = A047617(k). (End)
%F A047495 E.g.f.: (2 + sin(x) - cos(x) + (4*x - 1)*exp(x))/2. - _Ilya Gutkovskiy_, May 27 2016
%F A047495 Sum_{n>=1} (-1)^(n+1)/a(n) = 3*Pi/16 - (sqrt(2)-1)*log(2)/8 + sqrt(2)*log(2-sqrt(2))/4. - _Amiram Eldar_, Dec 25 2021
%p A047495 A047495:=n->(1+I)*(4*n-4*n*I+I-1+I^(1-n)-I^n)/4: seq(A047495(n), n=1..100); # _Wesley Ivan Hurt_, May 27 2016
%t A047495 Table[(1+I)*(4n-4n*I+I-1+I^(1-n)-I^n)/4, {n, 80}] (* _Wesley Ivan Hurt_, May 27 2016 *)
%o A047495 (Magma) [n : n in [0..150] | n mod 8 in [2, 4, 5, 7]]; // _Wesley Ivan Hurt_, May 27 2016
%Y A047495 Cf. A047535, A047617.
%K A047495 nonn,easy
%O A047495 1,1
%A A047495 _N. J. A. Sloane_