%I #20 Sep 08 2022 08:44:56
%S 0,1,2,3,6,7,8,9,10,13,14,15,16,17,20,21,22,23,24,27,28,29,30,31,34,
%T 35,36,37,38,41,42,43,44,45,48,49,50,51,52,55,56,57,58,59,62,63,64,65,
%U 66,69,70,71,72,73,76,77,78
%N Numbers that are congruent to {0, 1, 2, 3, 6} mod 7.
%H Vincenzo Librandi, <a href="/A047287/b047287.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F G.f.: x^2*(1+x+x^2+3*x^3+x^4)/((1-x)^2*(1+x+x^2+x^3+x^4)). [_Colin Barker_, May 14 2012]
%F a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6. _Vincenzo Librandi_, May 15 2012
%F a(n) = (7n - 5 - 2*(n mod 5)/5. - _Wesley Ivan Hurt_, Dec 28 2016
%t Select[Range[0,400],MemberQ[{0,1,2,3,6},Mod[#,7]]&] (* _Vincenzo Librandi_, May 15 2012 *)
%o (Magma) I:=[0, 1, 2, 3, 6, 7]; [n le 6 select I[n] else Self(n-1)+Self(n-5)-Self(n-6): n in [1..70]]; // _Vincenzo Librandi_, May 15 2012
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_
|