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%I #15 Sep 08 2022 08:44:56
%S 0,2,3,6,7,9,10,13,14,16,17,20,21,23,24,27,28,30,31,34,35,37,38,41,42,
%T 44,45,48,49,51,52,55,56,58,59,62,63,65,66,69,70,72,73,76,77,79,80,83,
%U 84,86,87,90,91,93,94,97,98,100,101,104,105,107,108,111
%N Numbers that are congruent to {0, 2, 3, 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+3*x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - _R. J. Mathar_, Oct 25 2011
%F From _Wesley Ivan Hurt_, Jun 02 2016: (Start)
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F a(n) = (14*n-13+3*i^(2*n)+(1+i)*i^(-n)+(1-i)*i^n)/8 where i=sqrt(-1).
%F a(2k) = A047276(k), a(2k-1) = A047355(k). (End)
%p A047285:=n->(14*n-13+3*I^(2*n)+(1+I)*I^(-n)+(1-I)*I^n)/8: seq(A047285(n), n=1..100); # _Wesley Ivan Hurt_, Jun 02 2016
%t Table[(14n-13+3*I^(2n)+(1+I)*I^(-n)+(1-I)*I^n)/8, {n, 80}] (* _Wesley Ivan Hurt_, Jun 02 2016 *)
%t Select[Range[0,120],MemberQ[{0,2,3,6},Mod[#,7]]&] (* or *) LinearRecurrence[ {1,0,0,1,-1},{0,2,3,6,7},100] (* _Harvey P. Dale_, Jul 12 2020 *)
%o (Magma) [n : n in [0..150] | n mod 7 in [0, 2, 3, 6]]; // _Wesley Ivan Hurt_, Jun 02 2016
%Y Cf. A047276, A047355.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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