# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a047477 Showing 1-1 of 1 %I A047477 #23 Sep 08 2022 08:44:57 %S A047477 0,5,7,8,13,15,16,21,23,24,29,31,32,37,39,40,45,47,48,53,55,56,61,63, %T A047477 64,69,71,72,77,79,80,85,87,88,93,95,96,101,103,104,109,111,112,117, %U A047477 119,120,125,127,128,133,135,136,141,143,144,149,151,152,157,159 %N A047477 Numbers that are congruent to {0, 5, 7} mod 8. %C A047477 Numbers m such that Lucas(m) mod 3 = 2. - _Bruno Berselli_, Oct 19 2017 %H A047477 Vincenzo Librandi, Table of n, a(n) for n = 1..1000 %H A047477 Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1). %F A047477 G.f.: x^2*(5+2*x+x^2)/((1-x)^2*(1+x+x^2)). - _Colin Barker_, May 14 2012 %F A047477 a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. - _Vincenzo Librandi_, May 16 2012 %F A047477 From _Wesley Ivan Hurt_, Jun 10 2016: (Start) %F A047477 a(n) = (24*n - 12 + 3*cos(2*n*Pi/3) - 7*sqrt(3)*sin(2*n*Pi/3))/9. %F A047477 a(3*k) = 8*k-1, a(3*k-1) = 8*k-3, a(3*k-2) = 8*k-8. (End) %p A047477 A047477:=n->(24*n-12+3*cos(2*n*Pi/3)-7*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047477(n), n=1..100); # _Wesley Ivan Hurt_, Jun 10 2016 %t A047477 Select[Range[0, 300], MemberQ[{0, 5, 7}, Mod[#, 8]] &] (* _Vincenzo Librandi_, May 16 2012 *) %o A047477 (Magma) I:=[0, 5, 7, 8]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // _Vincenzo Librandi_, May 16 2012 %Y A047477 Cf. A000032. %Y A047477 Cf. A016825: numbers m such that Lucas(m) mod 3 = 0. %Y A047477 Cf. A047459: numbers m such that Lucas(m) mod 3 = 1. %K A047477 nonn,easy %O A047477 1,2 %A A047477 _N. J. A. Sloane_ # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE