A047591 - OEIS

%I #11 Sep 08 2022 08:44:57

%S 1,6,7,9,14,15,17,22,23,25,30,31,33,38,39,41,46,47,49,54,55,57,62,63,

%T 65,70,71,73,78,79,81,86,87,89,94,95,97,102,103,105,110,111,113,118,

%U 119,121,126,127,129,134,135,137,142,143,145,150,151,153,158,159

%N Numbers that are congruent to {1, 6, 7} mod 8.

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

%F From _Wesley Ivan Hurt_, Jun 09 2016: (Start)

%F G.f.: x*(1+5*x+x^2+x^3)/((x-1)^2*(1+x+x^2)).

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

%F a(n) = (24*n-6-3*cos(2*n*Pi/3)-7*sqrt(3)*sin(2*n*Pi/3))/9.

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

%p A047591:=n->(24*n-6-3*cos(2*n*Pi/3)-7*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047591(n), n=1..100); # _Wesley Ivan Hurt_, Jun 09 2016

%t Select[Range[0, 150], MemberQ[{1, 6, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 09 2016 *)

%t #+{1,6,7}&/@(8*Range[0,20])//Flatten (* _Harvey P. Dale_, Jul 30 2022 *)

%o (Magma) [n : n in [0..150] | n mod 8 in [1, 6, 7]]; // _Wesley Ivan Hurt_, Jun 09 2016

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_