%I #16 Sep 08 2022 08:44:57

%S 0,1,7,8,9,15,16,17,23,24,25,31,32,33,39,40,41,47,48,49,55,56,57,63,

%T 64,65,71,72,73,79,80,81,87,88,89,95,96,97,103,104,105,111,112,113,

%U 119,120,121,127,128,129,135,136,137,143,144,145,151,152,153,159

%N Numbers that are congruent to {0, 1, 7} mod 8.

%H Vincenzo Librandi, <a href="/A047523/b047523.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).

%F G.f.: x^2*(1+6*x+x^2) / ((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Oct 08 2011

%F From _Wesley Ivan Hurt_, Jun 13 2016: (Start)

%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

%F a(n) = (24*n-24+15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*Pi*n/3))/9.

%F a(3k) = 8k-1, a(3k-1) = 8k-7, a(3k-2) = 8k-8. (End)

%p A047523:=n->(24*n-24+15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*Pi*n/3))/9: seq(A047523(n), n=1..100); # _Wesley Ivan Hurt_, Jun 13 2016

%t Select[Range[0, 150], MemberQ[{0, 1, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 13 2016 *)

%t LinearRecurrence[{1, 0, 1, -1}, {0, 1, 7, 8}, 100] (* _Vincenzo Librandi_, Jun 14 2016 *)

%o (Magma) [n : n in [0..150] | n mod 8 in [0, 1, 7]]; // _Wesley Ivan Hurt_, Jun 13 2016

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_