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%I #22 Sep 08 2022 08:44:57
%S 0,5,6,7,8,13,14,15,16,21,22,23,24,29,30,31,32,37,38,39,40,45,46,47,
%T 48,53,54,55,56,61,62,63,64,69,70,71,72,77,78,79,80,85,86,87,88,93,94,
%U 95,96,101,102,103,104,109,110,111,112,117,118,119,120,125
%N Numbers that are congruent to {0, 5, 6, 7} 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 From _Wesley Ivan Hurt_, May 29 2016: (Start)
%F G.f.: x^2*(5+x+x^2+x^3) / ((x-1)^2*(1+x+x^2+x^3)).
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F a(n) = (4*n-1+i^(2*n)-(1+i)*i^(-n)-(1-i)*i^n)/2 where i=sqrt(-1).
%F a(2k) = A047550(k), a(2k-1) = A047451(k). (End)
%F E.g.f.: 1 - sin(x) - cos(x) - sinh(x) + 2*x*exp(x). - _Ilya Gutkovskiy_, May 30 2016
%F Sum_{n>=2} (-1)^n/a(n) = 5*log(2)/8 - (2*sqrt(2)-1)*Pi/16. - _Amiram Eldar_, Dec 23 2021
%p A047575:=n->(4*n-1+I^(2*n)-(1+I)*I^(-n)-(1-I)*I^n)/2: seq(A047575(n), n=1..100); # _Wesley Ivan Hurt_, May 29 2016
%t Select[Range[0,120], MemberQ[{0,5,6,7}, Mod[#,8]]&] (* _Harvey P. Dale_, Jun 30 2011 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [0, 5, 6, 7]]; // _Wesley Ivan Hurt_, May 29 2016
%Y Cf. A047451, A047550.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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