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A047474 Numbers that are congruent to {0, 2, 3} mod 8. 1

%I #22 Sep 08 2022 08:44:57

%S 0,2,3,8,10,11,16,18,19,24,26,27,32,34,35,40,42,43,48,50,51,56,58,59,

%T 64,66,67,72,74,75,80,82,83,88,90,91,96,98,99,104,106,107,112,114,115,

%U 120,122,123,128,130,131,136,138,139,144,146,147,152,154,155

%N Numbers that are congruent to {0, 2, 3} mod 8.

%H Colin Barker, <a href="/A047474/b047474.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*(2+x+5*x^2)/((1-x)^2*(1+x+x^2)). - _Colin Barker_, May 13 2012

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

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

%F a(n) = (24*n-33-12*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9.

%F a(3k) = 8k-5, a(3k-1) = 8k-6, a(3k-2) = 8k-8. (End)

%p A047474:=n->(24*n-33-12*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047474(n), n=1..100); # _Wesley Ivan Hurt_, Jun 09 2016

%t Select[Range[0,150], MemberQ[{0,2,3}, Mod[#,8]]&] (* _Harvey P. Dale_, Apr 08 2013 *)

%o (Magma) [n : n in [0..150] | n mod 8 in [0, 2, 3]]; // _Wesley Ivan Hurt_, Jun 09 2016

%o (PARI) concat(0, Vec(x^2*(2+x+5*x^2)/((1-x)^2*(1+x+x^2)) + O(x^100))) \\ _Colin Barker_, Jun 12 2016

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_

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Last modified March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)