cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A047480 Numbers that are congruent to {2, 5, 7} mod 8.

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%I A047480 #21 Jan 31 2023 16:36:04
%S A047480 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 A047480 66,69,71,74,77,79,82,85,87,90,93,95,98,101,103,106,109,111,114,117,
%U A047480 119,122,125,127,130,133,135,138,141,143,146,149,151,154,157,159
%N A047480 Numbers that are congruent to {2, 5, 7} mod 8.
%H A047480 Vincenzo Librandi, <a href="/A047480/b047480.txt">Table of n, a(n) for n = 1..3000</a>
%H A047480 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A047480 G.f.: x*(1+x)*(x^2+x+2) / ((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Oct 08 2011
%F A047480 From _Wesley Ivan Hurt_, Jun 10 2016: (Start)
%F A047480 a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F A047480 a(n) = (24*n-6-3*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9.
%F A047480 a(3k) = 8k-1, a(3k-1) = 8k-3, a(3k-2) = 8k-6. (End)
%F A047480 a(n) = A047408(n) + 1. - _Lorenzo Sauras Altuzarra_, Jan 31 2023
%p A047480 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 A047480 Select[Range[0, 150], MemberQ[{2, 5, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 10 2016 *)
%t A047480 Flatten[Table[8 n + {2, 5, 7}, {n, 0, 150}]] (* _Vincenzo Librandi_, Jun 12 2016 *)
%t A047480 LinearRecurrence[{1,0,1,-1},{2,5,7,10},100] (* _Harvey P. Dale_, Jun 18 2018 *)
%o A047480 (Magma) [n : n in [0..150] | n mod 8 in [2, 5, 7]]; // _Wesley Ivan Hurt_, Jun 10 2016
%Y A047480 Different from A038127.
%Y A047480 Cf. A047408.
%K A047480 nonn,easy
%O A047480 1,1
%A A047480 _N. J. A. Sloane_