A047480 - OEIS

%I #21 Jan 31 2023 16:36:04

%S 2,5,7,10,13,15,18,21,23,26,29,31,34,37,39,42,45,47,50,53,55,58,61,63,

%T 66,69,71,74,77,79,82,85,87,90,93,95,98,101,103,106,109,111,114,117,

%U 119,122,125,127,130,133,135,138,141,143,146,149,151,154,157,159

%N Numbers that are congruent to {2, 5, 7} mod 8.

%H Vincenzo Librandi, <a href="/A047480/b047480.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 G.f.: x*(1+x)*(x^2+x+2) / ((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Oct 08 2011

%F From _Wesley Ivan Hurt_, Jun 10 2016: (Start)

%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)-sqrt(3)*sin(2*n*Pi/3))/9.

%F a(3k) = 8k-1, a(3k-1) = 8k-3, a(3k-2) = 8k-6. (End)

%F a(n) = A047408(n) + 1. - _Lorenzo Sauras Altuzarra_, Jan 31 2023

%p A047480:=n->(24*n-6-3*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9: seq(A047480(n), n=1..100); # _Wesley Ivan Hurt_, Jun 10 2016

%t Select[Range[0, 150], MemberQ[{2, 5, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 10 2016 *)

%t Flatten[Table[8 n + {2, 5, 7}, {n, 0, 150}]] (* _Vincenzo Librandi_, Jun 12 2016 *)

%t LinearRecurrence[{1,0,1,-1},{2,5,7,10},100] (* _Harvey P. Dale_, Jun 18 2018 *)

%o (Magma) [n : n in [0..150] | n mod 8 in [2, 5, 7]]; // _Wesley Ivan Hurt_, Jun 10 2016

%Y Different from A038127.

%Y Cf. A047408.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_