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%I #17 Sep 08 2022 08:44:57
%S 0,2,3,7,8,10,11,15,16,18,19,23,24,26,27,31,32,34,35,39,40,42,43,47,
%T 48,50,51,55,56,58,59,63,64,66,67,71,72,74,75,79,80,82,83,87,88,90,91,
%U 95,96,98,99,103,104,106,107,111,112,114,115,119,120,122,123
%N Numbers that are congruent to {0, 2, 3, 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*(2+x+4*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) = 2*n+(1+i)*(4*i-4+(1-i)*i^(2n)+i^(-n)-i^(1+n))/4 where i=sqrt(-1).
%F a(2k) = A047524(k), a(2k-1) = A047470(k). (End)
%F E.g.f.: (2 + sin(x) + cos(x) + (4*x - 5)*sinh(x) + (4*x - 3)*cosh(x))/2. - _Ilya Gutkovskiy_, May 29 2016
%F Sum_{n>=2} (-1)^n/a(n) = (3-sqrt(2))*log(2)/8 + sqrt(2)*log(2+sqrt(2))/4 - (2*sqrt(2)-1)*Pi/16. - _Amiram Eldar_, Dec 21 2021
%p A047532:=n->2*n+(1+I)*(4*I-4+(1-I)*I^(2*n)+I^(-n)-I^(1+n))/4: seq(A047532(n), n=1..100); # _Wesley Ivan Hurt_, May 29 2016
%t Table[2n+(1+I)*(4*I-4+(1-I)*I^(2n)+I^(-n)-I^(1+n))/4, {n, 80}] (* _Wesley Ivan Hurt_, May 29 2016 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [0, 2, 3, 7]]; // _Wesley Ivan Hurt_, May 29 2016
%Y Cf. A047470, A047524.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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