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A047460 Numbers that are congruent to {0, 1, 3, 4} mod 8.

%I A047460 #30 Sep 08 2022 08:44:57
%S A047460 0,1,3,4,8,9,11,12,16,17,19,20,24,25,27,28,32,33,35,36,40,41,43,44,48,
%T A047460 49,51,52,56,57,59,60,64,65,67,68,72,73,75,76,80,81,83,84,88,89,91,92,
%U A047460 96,97,99,100,104,105,107,108,112,113,115,116,120,121,123
%N A047460 Numbers that are congruent to {0, 1, 3, 4} mod 8.
%H A047460 Vincenzo Librandi, <a href="/A047460/b047460.txt">Table of n, a(n) for n = 1..1000</a>
%H A047460 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047460 From _Colin Barker_, May 14 2012: (Start)
%F A047460 a(n) = (-1/4+i/4)*((6+6*i)+(1+i)*(-1)^n+(-i)^n+i*i^n)+2*n where i=sqrt(-1).
%F A047460 G.f.: x^2*(1+2*x+x^2+4*x^3)/((1-x)^2*(1+x)*(1+x^2)). (End)
%F A047460 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - _Vincenzo Librandi_, May 16 2012
%F A047460 a(2k) = A047461(k), a(2k-1) = A047470(k). - _Wesley Ivan Hurt_, Jun 01 2016
%F A047460 Sum_{n>=2} (-1)^n/a(n) = Pi/8 + (2-sqrt(2))*log(2)/8 + sqrt(2)*log(2+sqrt(2))/4. - _Amiram Eldar_, Dec 20 2021
%p A047460 A047460:=n->(-1/4+I/4)*((6+6*I)+(1+I)*I^(2*n)+(-I)^n+I*I^n)+2*n: seq(A047460(n), n=1..100); # _Wesley Ivan Hurt_, Jun 01 2016
%t A047460 Select[Range[0,3000], MemberQ[{0,1,3,4}, Mod[#,8]]&] (* _Vincenzo Librandi_, May 16 2012 *)
%o A047460 (Magma) I:=[0, 1, 3, 4, 8]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // _Vincenzo Librandi_, May 16 2012
%o A047460 (PARI) my(x='x+O('x^100)); concat(0, Vec(x^2*(1+2*x+x^2+4*x^3)/((1-x)^2*(1+x)*(1+x^2)))) \\ _Altug Alkan_, Dec 24 2015
%Y A047460 Cf. A047461, A047470.
%K A047460 nonn,easy
%O A047460 1,3
%A A047460 _N. J. A. Sloane_