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A047445 Numbers that are congruent to {1, 3, 5, 6} mod 8.

%I A047445 #20 Sep 08 2022 08:44:57
%S A047445 1,3,5,6,9,11,13,14,17,19,21,22,25,27,29,30,33,35,37,38,41,43,45,46,
%T A047445 49,51,53,54,57,59,61,62,65,67,69,70,73,75,77,78,81,83,85,86,89,91,93,
%U A047445 94,97,99,101,102,105,107,109,110,113,115,117,118,121,123,125
%N A047445 Numbers that are congruent to {1, 3, 5, 6} mod 8.
%H A047445 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047445 G.f.: x*(1+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 A047445 From _Wesley Ivan Hurt_, May 26 2016: (Start)
%F A047445 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047445 a(n) = (8*n-5-i^(2*n)-i^(-n)-i^n)/4 where i=sqrt(-1).
%F A047445 a(2k) = A047398(k), a(2k-1) = A016813(k-1) for k>0. (End)
%F A047445 E.g.f.: (4 - cos(x) + (4*x - 2)*sinh(x) + (4*x - 3)*cosh(x))/2. - _Ilya Gutkovskiy_, May 27 2016
%F A047445 Sum_{n>=1} (-1)^(n+1)/a(n) = (4-sqrt(2))*Pi/16 + log(2)/8 + sqrt(2)*log(sqrt(2)+1)/8. - _Amiram Eldar_, Dec 24 2021
%p A047445 A047445:=n->(8*n-5-I^(2*n)-I^(-n)-I^n)/4: seq(A047445(n), n=1..100); # _Wesley Ivan Hurt_, May 26 2016
%t A047445 Table[(8n-5-I^(2n)-I^(-n)-I^n)/4, {n, 80}] (* _Wesley Ivan Hurt_, May 26 2016 *)
%o A047445 (Magma) [n : n in [0..150] | n mod 8 in [1, 3, 5, 6]]; // _Wesley Ivan Hurt_, May 26 2016
%Y A047445 Cf. A016813, A047398.
%K A047445 nonn,easy
%O A047445 1,2
%A A047445 _N. J. A. Sloane_