A047616 - OEIS

%I #17 Jul 20 2024 17:32:27

%S 0,1,5,8,9,13,16,17,21,24,25,29,32,33,37,40,41,45,48,49,53,56,57,61,

%T 64,65,69,72,73,77,80,81,85,88,89,93,96,97,101,104,105,109,112,113,

%U 117,120,121,125,128,129,133,136,137,141,144,145,149,152,153,157

%N Numbers that are congruent to {0, 1, 5} mod 8.

%H Vincenzo Librandi, <a href="/A047616/b047616.txt">Table of n, a(n) for n = 1..3000</a>

%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^2*(1+4*x+3*x^2)/((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-30+3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.

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

%p A047616:=n->(24*n-30+3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047616(n), n=1..100); # _Wesley Ivan Hurt_, Jun 09 2016

%t Select[Range[0, 150], MemberQ[{0, 1, 5}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 09 2016 *)

%t Table[8 n + {0, 1, 5}, {n, 0, 200}]//Flatten (* _Vincenzo Librandi_, Jun 11 2016 *)

%t LinearRecurrence[{1,0,1,-1},{0,1,5,8},60] (* _Harvey P. Dale_, Jul 20 2024 *)

%o (Magma) [n : n in [0..150] | n mod 8 in [0, 1, 5]]; // _Wesley Ivan Hurt_, Jun 09 2016

%o (PARI) a(n)=n\3*8+[-3,0,1][n%3+1] \\ _Charles R Greathouse IV_, Jul 19 2016

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_