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A047300 Numbers that are congruent to {2, 3, 4, 6} mod 7.

%I A047300 #13 Sep 08 2022 08:44:56
%S A047300 2,3,4,6,9,10,11,13,16,17,18,20,23,24,25,27,30,31,32,34,37,38,39,41,
%T A047300 44,45,46,48,51,52,53,55,58,59,60,62,65,66,67,69,72,73,74,76,79,80,81,
%U A047300 83,86,87,88,90,93,94,95,97,100,101,102,104,107,108,109,111
%N A047300 Numbers that are congruent to {2, 3, 4, 6} mod 7.
%H A047300 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047300 G.f.: x*(2+x+x^2+2*x^3+x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Oct 25 2011
%F A047300 From _Wesley Ivan Hurt_, Jun 02 2016: (Start)
%F A047300 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047300 a(n) = (14*n-5-i^(2*n)-(1-3*i)*i^(-n)-(1+3*i)*i^n)/8 where i=sqrt(-1).
%F A047300 a(2k) = A047280(k), a(2k-1) = A047348(k). (End)
%p A047300 A047300:=n->(14*n-5-I^(2*n)-(1-3*I)*I^(-n)-(1+3*I)*I^n)/8: seq(A047300(n), n=1..100); # _Wesley Ivan Hurt_, Jun 02 2016
%t A047300 Table[(14n-5-I^(2n)-(1-3*I)*I^(-n)-(1+3*I)*I^n)/8, {n, 80}] (* _Wesley Ivan Hurt_, Jun 02 2016 *)
%o A047300 (Magma) [n : n in [0..150] | n mod 7 in [2, 3, 4, 6]]; // _Wesley Ivan Hurt_, Jun 02 2016
%Y A047300 Cf. A047280, A047348.
%K A047300 nonn,easy
%O A047300 1,1
%A A047300 _N. J. A. Sloane_