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%I #31 Sep 08 2022 08:44:56
%S 1,4,5,6,8,11,12,13,15,18,19,20,22,25,26,27,29,32,33,34,36,39,40,41,
%T 43,46,47,48,50,53,54,55,57,60,61,62,64,67,68,69,71,74,75,76,78,81,82,
%U 83,85,88,89,90,92,95,96,97,99,102,103,104,106,109,110,111
%N Numbers that are congruent to {1, 4, 5, 6} mod 7.
%H Vincenzo Librandi, <a href="/A047313/b047313.txt">Table of n, a(n) for n = 1..1000</a>
%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*(1+3*x+x^2+x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - _R. J. Mathar_, Dec 03 2011
%F From _Wesley Ivan Hurt_, May 23 2016: (Start)
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F a(n) = (14n-3+i^(2n)-(3+i)*i^(-n)-(3-i)*i^n)/8 where i=sqrt(-1).
%F a(2n) = A047288(n), a(2n-1) = A047383(n). (End)
%F E.g.f.: (4 - sin(x) - 3*cos(x) + (7*x - 2)*sinh(x) + (7*x - 1)*cosh(x))/4. - _Ilya Gutkovskiy_, May 24 2016
%p A047313:= n-> iquo(n-1, 4, 'r')*7 +[1, 4, 5, 6][r+1]: seq(A047313(n), n=1..80); # _Alois P. Heinz_, Dec 04 2011
%t Select[Range[100],MemberQ[{1,4,5,6},Mod[#,7]]&] (* _Harvey P. Dale_, Apr 17 2011 *)
%t LinearRecurrence[{1, 0, 0, 1, -1}, {1, 4, 5, 6, 8}, 80] (* _Jean-François Alcover_, Feb 18 2016 *)
%o (Magma) [n : n in [0..150] | n mod 7 in [1, 4, 5, 6]]; // _Wesley Ivan Hurt_, May 23 2016
%Y Cf. A047288, A047383.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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