cp's OEIS Frontend

A047517 Numbers that are congruent to {0, 1, 3, 4, 6, 7} mod 8.

%I A047517 #36 Sep 08 2022 08:44:57
%S A047517 0,1,3,4,6,7,8,9,11,12,14,15,16,17,19,20,22,23,24,25,27,28,30,31,32,
%T A047517 33,35,36,38,39,40,41,43,44,46,47,48,49,51,52,54,55,56,57,59,60,62,63,
%U A047517 64,65,67,68,70,71,72,73,75,76,78,79,80,81,83,84,86,87,88,89
%N A047517 Numbers that are congruent to {0, 1, 3, 4, 6, 7} mod 8.
%H A047517 G. C. Greubel, <a href="/A047517/b047517.txt">Table of n, a(n) for n = 1..1000</a>
%H A047517 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%F A047517 From _Chai Wah Wu_, May 30 2016: (Start)
%F A047517 a(n) = a(n-1) + a(n-6) - a(n-7), for n > 7.
%F A047517 G.f.: x^2*(x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^7 - x^6 - x + 1). (End)
%F A047517 From _Wesley Ivan Hurt_, Jun 16 2016: (Start)
%F A047517 a(n) = (24*n-21-3*cos(n*Pi)+2*sqrt(3)*cos((1+4*n)*Pi/6)+6*sin((1-2*n)*Pi/6))/18.
%F A047517 a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-4, a(6k-3) = 8k-5, a(6k-4) = 8k-7, a(6k-5) = 8k-8. (End)
%F A047517 Sum_{n>=2} (-1)^n/a(n) = (2-sqrt(2))*Pi/16 + (6-3*sqrt(2))*log(2)/16 + 3*sqrt(2)*log(sqrt(2)+2)/8. - _Amiram Eldar_, Dec 27 2021
%p A047517 A047424:=n->(24*n-21-3*cos(n*Pi)+2*sqrt(3)*cos((1+4*n)*Pi/6)+6*sin((1-2*n)* Pi/6))/18: seq(A047424(n), n=1..100); # _Wesley Ivan Hurt_, Jun 16 2016
%t A047517 LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 3, 4, 6, 7, 8}, 50] (* _G. C. Greubel_, May 30 2016 *)
%t A047517 Select[Range[0,200], MemberQ[{0, 1, 3, 4, 6, 7}, Mod[#, 8]] &] (* _Vincenzo Librandi_, May 30 2016 *)
%o A047517 (Magma) [n: n in [0..110] | n mod 8 in [0,1,3,4,6,7]]; // _Vincenzo Librandi_, May 30 2016
%o A047517 (PARI) my(x='x+O('x^50)); concat([0], Vec(x^2*(x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^7 - x^6 - x + 1))) \\ _G. C. Greubel_, Oct 29 2017
%Y A047517 Cf. A047428, A047585.
%K A047517 nonn,easy
%O A047517 1,3
%A A047517 _N. J. A. Sloane_