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A047307 Numbers that are congruent to {3, 4, 5, 6} mod 7.

%I A047307 #15 Dec 28 2024 18:11:38
%S A047307 3,4,5,6,10,11,12,13,17,18,19,20,24,25,26,27,31,32,33,34,38,39,40,41,
%T A047307 45,46,47,48,52,53,54,55,59,60,61,62,66,67,68,69,73,74,75,76,80,81,82,
%U A047307 83,87,88,89,90,94,95,96,97,101,102,103,104,108,109,110,111
%N A047307 Numbers that are congruent to {3, 4, 5, 6} mod 7.
%H A047307 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047307 G.f.: x*(3+x+x^2+x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - _R. J. Mathar_, Oct 25 2011
%F A047307 From _Wesley Ivan Hurt_, Jun 02 2016: (Start)
%F A047307 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047307 a(n) = (14*n+1-3*i^(2*n)-(3-3*i)*i^(-n)-(3+3*i)*i^n)/8 where i=sqrt(-1).
%F A047307 a(2k) = A047288(k), a(2k-1) = A047389(k). (End)
%p A047307 A047307:=n->(14*n+1-3*I^(2*n)-(3-3*I)*I^(-n)-(3+3*I)*I^n)/8: seq(A047307(n), n=1..100); # _Wesley Ivan Hurt_, Jun 02 2016
%t A047307 Table[(14n+1-3*I^(2*n)-(3-3*I)*I^(-n)-(3+3*I)*I^n)/8, {n, 80}] (* _Wesley Ivan Hurt_, Jun 02 2016 *)
%t A047307 LinearRecurrence[{1,0,0,1,-1},{3,4,5,6,10},70] (* _Harvey P. Dale_, Dec 28 2024 *)
%o A047307 (Magma) [n : n in [0..150] | n mod 7 in [3, 4, 5, 6]]; // _Wesley Ivan Hurt_, Jun 02 2016
%Y A047307 Cf. A047288, A047389.
%K A047307 nonn,easy
%O A047307 1,1
%A A047307 _N. J. A. Sloane_