cp's OEIS Frontend

A047622 Numbers that are congruent to {0, 3, 5} mod 8.

%I A047622 #25 Mar 31 2023 05:13:47
%S A047622 0,3,5,8,11,13,16,19,21,24,27,29,32,35,37,40,43,45,48,51,53,56,59,61,
%T A047622 64,67,69,72,75,77,80,83,85,88,91,93,96,99,101,104,107,109,112,115,
%U A047622 117,120,123,125,128,131,133,136,139,141,144,147,149,152,155,157
%N A047622 Numbers that are congruent to {0, 3, 5} mod 8.
%H A047622 Vincenzo Librandi, <a href="/A047622/b047622.txt">Table of n, a(n) for n = 1..1000</a>
%H A047622 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A047622 From _R. J. Mathar_, Oct 18 2008: (Start)
%F A047622 G.f.: x^2*(3+2*x+3*x^2)/((1-x)^2*(1+x+x^2)).
%F A047622 a(n) = A008576(n-1), for n>1. (End)
%F A047622 a(n) = floor((8n-7)/3). - _Gary Detlefs_, Mar 07 2010
%F A047622 From _Wesley Ivan Hurt_, Jun 13 2016: (Start)
%F A047622 a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F A047622 a(n) = (24*n-24-3*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9.
%F A047622 a(3k) = 8k-3, a(3k-1) = 8k-5, a(3k-2) = 8k-8. (End)
%F A047622 a(n) = A047408(n) - 1. - _Lorenzo Sauras Altuzarra_, Jan 31 2023
%F A047622 E.g.f.: 3 + (8/3)*exp(x)*(x - 1) - exp(-x/2)*(3*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2))/9. - _Stefano Spezia_, Mar 30 2023
%p A047622 seq(floor((8*n-7)/3), n=1..52); # _Gary Detlefs_, Mar 07 2010
%t A047622 Select[Range[0,150], MemberQ[{0,3,5}, Mod[#,8]]&] (* _Harvey P. Dale_, Oct 04 2012 *)
%t A047622 LinearRecurrence[{1, 0, 1, -1}, {0, 3, 5, 8}, 100] (* _Vincenzo Librandi_, Jun 14 2016 *)
%o A047622 (Magma) [n : n in [0..150] | n mod 8 in [0, 3, 5]]; // _Wesley Ivan Hurt_, Jun 13 2016
%Y A047622 Cf. A008576, A047408.
%K A047622 nonn,easy
%O A047622 1,2
%A A047622 _N. J. A. Sloane_