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%I #20 Sep 08 2022 08:44:56
%S 1,2,5,6,8,9,12,13,15,16,19,20,22,23,26,27,29,30,33,34,36,37,40,41,43,
%T 44,47,48,50,51,54,55,57,58,61,62,64,65,68,69,71,72,75,76,78,79,82,83,
%U 85,86,89,90,92,93,96,97,99,100,103,104,106,107,110,111
%N Numbers that are congruent to {1, 2, 5, 6} mod 7.
%H Vincenzo Librandi, <a href="/A047325/b047325.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+x+3*x^2+x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - _R. J. Mathar_, Dec 04 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-7-3*i^(2n)+(1-i)*i^(-n)+(1+i)*i^n)/8 where i=sqrt(-1).
%F a(2n) = A047276(n), a(2n-1) = A047383(n). (End)
%F E.g.f.: (4 - sin(x) + cos(x) + (7*x - 2)*sinh(x) + (7*x - 5)*cosh(x))/4. - _Ilya Gutkovskiy_, May 24 2016
%p A047325:=n->(14*n-7-3*I^(2*n)+(1-I)*I^(-n)+(1+I)*I^n)/8: seq(A047325(n), n=1..100); # _Wesley Ivan Hurt_, May 23 2016
%t Table[(14n-7-3*I^(2n)+(1-I)*I^(-n)+(1+I)*I^n)/8, {n, 80}] (* _Wesley Ivan Hurt_, May 23 2016 *)
%t LinearRecurrence[{1, 0, 0, 1, -1}, {1, 2, 5, 6, 8}, 80] (* _Vincenzo Librandi_, May 24 2016 *)
%t #+{1,2,5,6}&/@(7*Range[0,20])//Flatten (* _Harvey P. Dale_, Aug 16 2018 *)
%o (Magma) [n : n in [0..150] | n mod 7 in [1, 2, 5, 6]]; // _Wesley Ivan Hurt_, May 23 2016
%Y Cf. A047276, A047383.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Wesley Ivan Hurt_, May 23 2016
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