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%I #15 Sep 08 2022 08:44:56
%S 2,4,5,6,9,11,12,13,16,18,19,20,23,25,26,27,30,32,33,34,37,39,40,41,
%T 44,46,47,48,51,53,54,55,58,60,61,62,65,67,68,69,72,74,75,76,79,81,82,
%U 83,86,88,89,90,93,95,96,97,100,102,103,104,107,109,110,111
%N Numbers that are congruent to {2, 4, 5, 6} mod 7.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F G.f.: x*(2+2*x+x^2+x^3+x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 03 2011
%F From _Wesley Ivan Hurt_, Jun 03 2016: (Start)
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F a(n) = (14*n-1-i^(2*n)-(3-i)*i^(-n)-(3+i)*i^n)/8 where i=sqrt(-1).
%F a(2k) = A047288(k), a(2k-1) = A047385(k). (End)
%p A047315:=n->(14*n-1-I^(2*n)-(3-I)*I^(-n)-(3+I)*I^n)/8: seq(A047315(n), n=1..100); # _Wesley Ivan Hurt_, Jun 03 2016
%t Table[(14n-1-I^(2n)-(3-I)*I^(-n)-(3+I)*I^n)/8, {n, 80}] (* _Wesley Ivan Hurt_, Jun 03 2016 *)
%t Select[Range[200],MemberQ[{2,4,5,6},Mod[#,7]]&] (* or *) LinearRecurrence[ {1,0,0,1,-1},{2,4,5,6,9},100] (* _Harvey P. Dale_, Jan 19 2019 *)
%o (Magma) [n : n in [0..150] | n mod 7 in [2, 4, 5, 6]]; // _Wesley Ivan Hurt_, Jun 03 2016
%Y Cf. A047288, A047385.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
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