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%I #35 Sep 08 2022 08:44:57
%S 0,2,5,8,10,13,16,18,21,24,26,29,32,34,37,40,42,45,48,50,53,56,58,61,
%T 64,66,69,72,74,77,80,82,85,88,90,93,96,98,101,104,106,109,112,114,
%U 117,120,122,125,128,130,133,136,138,141,144,146,149,152,154,157,160,162
%N Numbers that are congruent to {0, 2, 5} mod 8.
%H Vincenzo Librandi, <a href="/A047618/b047618.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 a(n) = 3*(n - 1) - floor((n - 1)/3) - ((n - 1)^2 % 3). - _Gary Detlefs_, Mar 19 2010; corrected by _L. Edson Jeffery_, Sep 02 2014
%F a(n) = floor(8*(n-1)/3). - _Gary Detlefs_, Jan 02 2012
%F G.f.: x^2*(2+3*x+3*x^2)/((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Feb 03 2014
%F Conjecture: a(n)+a(n+1)+a(n+2) = 8*n-1; or a(n) = 8*(n-2)-a(n-1)-a(n-2)-1, n>3, with a(1)=0, a(2)=2, a(3)=5. - _L. Edson Jeffery_, Sep 02 2014
%F a(n) = a(n-1)+a(n-3)-a(n-4), n>4, with a(1)=0, a(2)=2, a(3)=5, a(4)=8. - _L. Edson Jeffery_, Sep 02 2014
%F a(n) = ((8*n-9)+2*sin((2*n*Pi)/3)/sqrt(3))/3. - _L. Edson Jeffery_, Sep 02 2014
%F a(3k) = 8k-3, a(3k-1) = 8k-6, a(3k-2) = 8k-8. - _Wesley Ivan Hurt_, Jun 10 2016
%p seq(3*n - floor(n/3) - (n^2 mod 3), n=0..51); # _Gary Detlefs_, Mar 19 2010
%t LinearRecurrence[{1, 0, 1, -1}, {0, 2, 5, 8}, 62] (* _L. Edson Jeffery_, Sep 02 2014 *)
%t Table[((8*n-9)+2*Sin[(2*n*Pi)/3]/Sqrt[3])/3, {n, 62}] (* _L. Edson Jeffery_, Sep 02 2014 *)
%t Table[8 n + {0, 2, 5}, {n, 0, 100}]//Flatten (* _Vincenzo Librandi_, Jun 11 2016 *)
%o (PARI) a(n) = floor(8*(n-1)/3); \\ _Michel Marcus_, Sep 03 2014
%o (Magma) [n : n in [0..150] | n mod 8 in [0, 2, 5]]; // _Wesley Ivan Hurt_, Jun 10 2016
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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