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%I #38 Feb 27 2023 04:01:02
%S 5,13,23,31,41,49,59,67,77,85,95,103,113,121,131,139,149,157,167,175,
%T 185,193,203,211,221,229,239,247,257,265,275,283,293,301,311,319,329,
%U 337,347,355,365,373,383,391,401,409,419,427,437,445,455,463,473,481
%N Numbers congruent to {5, 13} mod 18.
%H Michael De Vlieger, <a href="/A143988/b143988.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n) = 18*(n-1) - a(n-1) for n > 1 and a(1)=5. - _Vincenzo Librandi_, Nov 25 2010
%F From _Colin Barker_, Oct 25 2019: (Start)
%F G.f.: x*(5 + 8*x + 5*x^2) / ((1 - x)^2*(1 + x)).
%F a(n) = a(n-1) + a(n-2) - a(n-3) for n>3.
%F a(n) = ((-1)^(1+n) + 18*n - 9) / 2. (End)
%F E.g.f.: 5 + ((18*x - 9)*exp(x) - exp(-x))/2. - _David Lovler_, Sep 08 2022
%F Sum_{n>=1} (-1)^(n+1)/a(n) = tan(2*Pi/9)*Pi/18. - _Amiram Eldar_, Feb 27 2023
%t Select[Range@ 500, MemberQ[{5, 13}, Mod[#, 18]] &] (* _Michael De Vlieger_, Nov 23 2018 *)
%o (GAP) Filtered([1..500],k->k mod 18 = 5 or k mod 18 = 13); # _Muniru A Asiru_, Nov 24 2018
%o (PARI) Vec(x*(5 + 8*x + 5*x^2) / ((1 - x)^2*(1 + x)) + O(x^60)) \\ _Colin Barker_, Oct 25 2019
%K nonn,easy
%O 1,1
%A _Giovanni Teofilatto_, Sep 07 2008
%E Corrected (213 replaced with 211, 231 with 229, 249 with 247, 265 with 267 etc.) by _R. J. Mathar_, Apr 22 2010
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