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A047553 Numbers that are congruent to {0, 2, 6, 7} mod 8.

%I A047553 #18 Sep 08 2022 08:44:57
%S A047553 0,2,6,7,8,10,14,15,16,18,22,23,24,26,30,31,32,34,38,39,40,42,46,47,
%T A047553 48,50,54,55,56,58,62,63,64,66,70,71,72,74,78,79,80,82,86,87,88,90,94,
%U A047553 95,96,98,102,103,104,106,110,111,112,114,118,119,120,122,126
%N A047553 Numbers that are congruent to {0, 2, 6, 7} mod 8.
%H A047553 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047553 From _Wesley Ivan Hurt_, May 29 2016: (Start)
%F A047553 G.f.: x^2*(2+4*x+x^2+x^3) / ((x-1)^2*(1+x+x^2+x^3)).
%F A047553 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047553 a(n) = (8*n-5-i^(2*n)+(1-2*i)*i^(-n)+(1+2*i)*i^n)/4 where i=sqrt(-1).
%F A047553 a(2k) = A047524(k), a(2k-1) = A047451(k). (End)
%F A047553 E.g.f.: (2 - 2*sin(x) + cos(x) + (4*x - 2)*sinh(x) + (4*x - 3)*cosh(x))/2. - _Ilya Gutkovskiy_, May 29 2016
%F A047553 Sum_{n>=2} (-1)^n/a(n) = (8-sqrt(2))*log(2)/16 + sqrt(2)*log(2+sqrt(2))/8 - (sqrt(2)-1)*Pi/16. - _Amiram Eldar_, Dec 21 2021
%p A047553 A047553:=n->(8*n-5-I^(2*n)+(1-2*I)*I^(-n)+(1+2*I)*I^n)/4: seq(A047553(n), n=1..100); # _Wesley Ivan Hurt_, May 29 2016
%t A047553 Select[Range[0,200], MemberQ[{0,2,6,7}, Mod[#,8]]&] (* _Harvey P. Dale_, Aug 09 2013 *)
%o A047553 (Magma) [n : n in [0..150] | n mod 8 in [0, 2, 6, 7]]; // _Wesley Ivan Hurt_, May 29 2016
%Y A047553 Cf. A047451, A047524.
%K A047553 nonn,easy
%O A047553 1,2
%A A047553 _N. J. A. Sloane_