cp's OEIS Frontend

A047428 Numbers that are congruent to {0, 1, 3, 4, 5, 6} mod 8.

%I A047428 #19 Sep 08 2022 08:44:57
%S A047428 0,1,3,4,5,6,8,9,11,12,13,14,16,17,19,20,21,22,24,25,27,28,29,30,32,
%T A047428 33,35,36,37,38,40,41,43,44,45,46,48,49,51,52,53,54,56,57,59,60,61,62,
%U A047428 64,65,67,68,69,70,72,73,75,76,77,78,80,81,83,84,85,86,88
%N A047428 Numbers that are congruent to {0, 1, 3, 4, 5, 6} mod 8.
%H A047428 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%F A047428 G.f.: x^2*(1+2*x+x^2+x^3+x^4+2*x^5) / ((1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2). - _R. J. Mathar_, Dec 07 2011
%F A047428 From _Wesley Ivan Hurt_, Jun 16 2016: (Start)
%F A047428 a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
%F A047428 a(n) = (24*n-27-3*cos(n*Pi)-6*cos(n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/18.
%F A047428 a(6k) = 8k-2, a(6k-1) = 8k-3, a(6k-2) = 8k-4, a(6k-3) = 8k-5, a(6k-4) = 8k-7, a(6k-5) = 8k-8. (End)
%F A047428 Sum_{n>=2} (-1)^n/a(n) = sqrt(2)*Pi/16 + log(2)/8 - sqrt(2)*log(99-70*sqrt(2))/16. - _Amiram Eldar_, Dec 27 2021
%p A047428 A047428:=n->(24*n-27-3*cos(n*Pi)-6*cos(n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/18: seq(A047428(n), n=1..100); # _Wesley Ivan Hurt_, Jun 16 2016
%t A047428 Select[Range[0, 100], MemberQ[{0, 1, 3, 4, 5, 6}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 16 2016 *)
%o A047428 (Magma) [n : n in [0..100] | n mod 8 in [0, 1, 3, 4, 5, 6]]; // _Wesley Ivan Hurt_, Jun 16 2016
%Y A047428 Cf. A047517, A047585.
%K A047428 nonn,easy
%O A047428 1,3
%A A047428 _N. J. A. Sloane_