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%I #19 Sep 08 2022 08:44:56
%S 1,3,4,6,8,10,11,13,15,17,18,20,22,24,25,27,29,31,32,34,36,38,39,41,
%T 43,45,46,48,50,52,53,55,57,59,60,62,64,66,67,69,71,73,74,76,78,80,81,
%U 83,85,87,88,90,92,94,95,97,99,101,102,104,106,108,109,111
%N Numbers that are congruent to {1, 3, 4, 6} mod 7.
%H Vincenzo Librandi, <a href="/A047298/b047298.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 a(n) = ceiling(ceiling((7n + 2)/2)/2).
%F G.f.: x*(1+2*x+x^2+2*x^3+x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Oct 25 2011
%F From _Wesley Ivan Hurt_, May 22 2016: (Start)
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F a(n) = i^(-n)*(i-1-7*i^n+14*n*i^n-(1+i)*i^(2n)+i^(-n))/8 where i=sqrt(-1).
%F a(2n) = A047280(n), a(2n-1) = A047346(n). (End)
%F E.g.f.: (4 + sin(x) - cos(x) + (7*x - 4)*sinh(x) + (7*x - 3)*cosh(x))/4. - _Ilya Gutkovskiy_, May 23 2016
%p A047298:=n->I^(-n)*(I-1-7*I^n+14*n*I^n-(1+I)*I^(2*n)+I^(-n))/8: seq(A047298(n), n=1..100); # _Wesley Ivan Hurt_, May 22 2016
%t Table[I^(-n)*(I-1-7I^n+14n*I^n-(1+I)*I^(2n)+I^(-n))/8, {n, 80}] (* _Wesley Ivan Hurt_, May 22 2016 *)
%t LinearRecurrence[{1, 0, 0, 1, -1}, {1, 3, 4, 6, 8}, 80] (* _Vincenzo Librandi_, May 24 2016 *)
%o (Magma) [n : n in [0..150] | n mod 7 in [1, 3, 4, 6]]; // _Wesley Ivan Hurt_, May 22 2016
%Y Cf. A047280, A047346.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Wesley Ivan Hurt_, May 22 2016
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