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A047216 Numbers that are congruent to {1, 2} mod 5. 24

%I

%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 <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)

%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. A047209, A047211, A047212, A176059.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_

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Last modified April 7 13:36 EDT 2020. Contains 333305 sequences. (Running on oeis4.)