%I #38 Aug 23 2022 21:25:42
%S 1,2,6,7,11,12,16,17,21,22,26,27,31,32,36,37,41,42,46,47,51,52,56,57,
%T 61,62,66,67,71,72,76,77,81,82,86,87,91,92,96,97,101,102,106,107,111,
%U 112,116,117,121,122,126,127,131,132,136,137,141,142,146,147
%N Numbers that are congruent to {1, 2} mod 5.
%C Equivalently, numbers ending in 1, 2, 6 and 7. - _Bruno Berselli_, Sep 04 2018
%H David Lovler, <a href="/A047216/b047216.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n) = 5*n-a(n-1)-7 for n>1, with a(1)=1. - _Vincenzo Librandi_, Aug 05 2010
%F G.f.: x*(1+x+3*x^2) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Oct 08 2011
%F From _Bruno Berselli_, Mar 10 2012: (Start)
%F a(n) = (10*n-3*(-1)^n-9)/4.
%F a(n) = - A176059(n) + Sum_{i=0..n-1} A176059(i). (End)
%F From _Wesley Ivan Hurt_, Dec 29 2016: (Start)
%F a(n) = a(n-1) + a(n-2) - a(n-3) for n > 3.
%F a(2*k) = 5*k-3, a(2*k-1) = 5*k-4. (End)
%F Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2-2*sqrt(5)/5)*Pi/10 + log(phi)/sqrt(5), where phi is the golden ratio (A001622). - _Amiram Eldar_, Dec 07 2021
%F E.g.f.: 3 + ((5*x - 9/2)*exp(x) - (3/2)*exp(-x))/2. - _David Lovler_, Aug 23 2022
%p A047216:=n->(10*n-3*(-1)^n-9)/4: seq(A047216(n), n=1..100); # _Wesley Ivan Hurt_, Dec 29 2016
%t Select[Range[0, 200], MemberQ[{1, 2}, Mod[#, 5]] &] (* _Vladimir Joseph Stephan Orlovsky_, Feb 12 2012 *)
%o (PARI) a(n)=(n-1)\2*5+2-n%2 \\ _Charles R Greathouse IV_, Dec 22 2011
%o (Magma) [(10*n-3*(-1)^n-9)/4 : n in [1..100]]; // _Wesley Ivan Hurt_, Dec 29 2016
%Y Cf. A001622, A047209, A047211, A047212, A176059.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_