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%I #71 Aug 23 2022 06:25:44
%S 0,3,5,8,10,13,15,18,20,23,25,28,30,33,35,38,40,43,45,48,50,53,55,58,
%T 60,63,65,68,70,73,75,78,80,83,85,88,90,93,95,98,100,103,105,108,110,
%U 113,115,118,120,123,125,128,130,133,135,138,140,143,145,148
%N Numbers that are congruent to {0, 3} mod 5.
%C Multiples of 5 interleaved with 2 less than multiples of 5. - _Wesley Ivan Hurt_, Oct 19 2013
%C Numbers k such that k^2/5 + k*(k + 1)/10 = k*(3*k + 1)/10 is a nonnegative integer. - _Bruno Berselli_, Feb 14 2017
%H N. J. A. Sloane, <a href="/A047218/b047218.txt">Table of n, a(n) for n = 1..10001</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n) = 2*n - 5 + ceiling(n/2). - Jesus De Loera (deloera(AT)math.ucdavis.edu)
%F a(n) = 5*n - a(n-1) - 7 for n>1, a(1)=0. - _Vincenzo Librandi_, Aug 05 2010
%F From _Bruno Berselli_, Jun 28 2011: (Start)
%F G.f.: (2*x + 3)*x^2/((x + 1)*(x - 1)^2).
%F a(n) = (10*n + (-1)^n - 9)/4.
%F a(n) = a(n-1) + a(n-2) - a(n-3). (End)
%F a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=3 and b(k)=A020714(k-1)=5*2^(k-1) for k>0. - _Philippe Deléham_, Oct 17 2011
%F a(n) = n + ceiling(3*(n-1)/2) - 1. - _Arkadiusz Wesolowski_, Sep 18 2012
%F a(n) = floor(5*n/2)-2 = 3*n - 3 - floor((n-1)/2). - _Wesley Ivan Hurt_, Oct 14 2013
%F a(n+1) = n + (n + (n + (n mod 2))/2). - _Wesley Ivan Hurt_, Oct 19 2013
%F Sum_{n>=2} (-1)^n/a(n) = log(5)/4 - sqrt(5)*log(phi)/10 - sqrt(1-2/sqrt(5))*Pi/10, where phi is the golden ratio (A001622). - _Amiram Eldar_, Dec 07 2021
%F E.g.f.: 2 + ((5*x - 9/2)*exp(x) + (1/2)*exp(-x))/2. - _David Lovler_, Aug 22 2022
%p seq(floor(5*k/2)-2, k=1..100); # _Wesley Ivan Hurt_, Sep 27 2013
%t Select[Range[0, 200], MemberQ[{0, 3}, Mod[#, 5]] &] (* _Vladimir Joseph Stephan Orlovsky_, Feb 12 2012 *)
%t Table[Floor[5 n/2] - 2, {n,100}] (* _Wesley Ivan Hurt_, Sep 27 2013 *)
%t With[{c5=5*Range[0,30]},Riffle[c5,c5+3]] (* or *) LinearRecurrence[{1,1,-1},{0,3,5},60] (* _Harvey P. Dale_, Apr 02 2017 *)
%o (PARI) forstep(n=0,200,[3,2],print1(n", ")) \\ _Charles R Greathouse IV_, Oct 17 2011
%Y Cf. A001622, A047211, A047212, A047216.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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