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%I #53 Aug 08 2022 20:25:26
%S 0,1,19,20,38,39,57,58,76,77,95,96,114,115,133,134,152,153,171,172,
%T 190,191,209,210,228,229,247,248,266,267,285,286,304,305,323,324,342,
%U 343,361,362,380,381,399,400,418,419,437,438,456,457,475,476,494,495,513,514,532
%N Numbers congruent to {0, 1} (mod 19).
%C Numbers m such that m^2 - m is divisible by 19.
%H David Lovler, <a href="/A151979/b151979.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+1) = Sum_k>=0 {A030308(n,k)*b(k)} with b(0)=1 and b(k)=19*2^(k-1) for k>0. - _Philippe Deléham_, Oct 19 2011
%F G.f.: x^2*(1+18*x)/((1-x)^2*(1+x)). - _Colin Barker_, Apr 09 2012
%F a(n) = a(n-1) + a(n-2) - a(n-3). - _Colin Barker_, Apr 09 2012
%F From _Stefano Spezia_, Feb 01 2020: (Start)
%F a(n) = (1/4)*(38*n - 55 - 17*(-1)^n).
%F E.g.f.: (19/2)*(x*(cosh(x) + sinh(x)) - sinh(x)) - 18*(cosh(x) - 1). (End)
%t Select[Range[0,600],MemberQ[{0,1},Mod[#,19]]&] (* _Harvey P. Dale_, Feb 11 2019 *)
%o (Magma) [n : n in [0..600] | n mod 19 in [0, 1]]; // _Vincenzo Librandi_, Feb 04 2020
%o (PARI) a(n) = (1/4)*(38*n - 55 - 17*(-1)^n); \\ _David Lovler_, Jul 25 2022
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_, Aug 23 2009