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A047444 Numbers that are congruent to {0, 3, 5, 6} mod 8.

%I A047444 #24 Sep 08 2022 08:44:57
%S A047444 0,3,5,6,8,11,13,14,16,19,21,22,24,27,29,30,32,35,37,38,40,43,45,46,
%T A047444 48,51,53,54,56,59,61,62,64,67,69,70,72,75,77,78,80,83,85,86,88,91,93,
%U A047444 94,96,99,101,102,104,107,109,110,112,115,117,118,120,123,125
%N A047444 Numbers that are congruent to {0, 3, 5, 6} mod 8.
%H A047444 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-1).
%F A047444 G.f.: x^2*(3-x+2*x^2) / ( (x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 07 2011
%F A047444 From _Wesley Ivan Hurt_, May 26 2016: (Start)
%F A047444 a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.
%F A047444 a(n) = (1+i)*(4*n-4*n*i+3*i-3-i^(-n)+i^(1+n))/4 where i=sqrt(-1).
%F A047444 a(2k) = A047398(k), a(2k-1) = A047645(k). (End)
%F A047444 E.g.f.: (4 - sin(x) - cos(x) + (4*x - 3)*exp(x))/2. - _Ilya Gutkovskiy_, May 27 2016
%F A047444 Sum_{n>=2} (-1)^n/a(n) = 3*log(2)/8 - (3-2*sqrt(2))*Pi/16. - _Amiram Eldar_, Dec 21 2021
%p A047444 A047444:=n->(1+I)*(4*n-4*n*I+3*I-3-I^(-n)+I^(1+n))/4: seq(A047444(n), n=1..100); # _Wesley Ivan Hurt_, May 26 2016
%t A047444 Table[(1+I)*(4n-4*n*I+3*I-3-I^(-n)+I^(1+n))/4, {n, 80}] (* _Wesley Ivan Hurt_, May 26 2016 *)
%t A047444 LinearRecurrence[{2,-2,2,-1},{0,3,5,6},70] (* _Harvey P. Dale_, Aug 26 2019 *)
%o A047444 (Magma) [n : n in [0..150] | n mod 8 in [0, 3, 5, 6]]; // _Wesley Ivan Hurt_, May 26 2016
%Y A047444 Cf. A047398, A047645.
%K A047444 nonn,easy
%O A047444 1,2
%A A047444 _N. J. A. Sloane_